Григорий Ольшанский

профессор / Сколковский институт науки и технологий
профессор / Национальный исследовательский университет “Высшая школа экономики” / факультет математики
главный научный сотрудник / Институт проблем передачи информации РАН

Профессиональные интересы
теория представлений (главным образом, бесконечномерных групп) и связанные с ней вопросы алгебраической комбинаторики (теория симметрических функций) и теории вероятностей (случайные разбиения, случайные точечные процессы)

Публикации

  1. G. Olshanski, N. Safonkin, "Remarks on Yangian-type algebras and double Poisson brackets"
    (“Замечания о янгианоподобных алгебрах и двойных скобках Пуассона”) Functional Analysis and its Applications, 2023, v. 57(4), pp. 75-88, doi.org/10.4213/faa4150 [ PDF: English, arXiv: 2308.13325]
  2. G. Olshanski, "Characters of classical groups, Schur-type functions, and discrete splines" (“Характеры классических групп, функции типа Шура и дискретные сплайны”) Matematicheskii Sbornik, 2023, v.214(11), pp. 89–132, doi.org/10.4213/sm9905 [ PDF: English, arXiv: 2307.05160]
  3. C. Cuenca, G. Olshanski, "Mackey-type identity for invariant functions on Lie algebras of finite unitary groups and an application ", Journal of Lie Theory 33 (2023), 149-168 www.heldermann.de/JLT/JLT33/JLT331/jlt33007.htm [ PDF: English, arXiv: 2206.07320]
  4. G. Olshanski, N. Safonkin, "Double Poisson brackets and involutive representation spaces" [ PDF: English, arXiv: 2310.01086]
  5. A. Bufetov, G. Olshanski, “A hierarchy of Palm measures for determinantal point processes with gamma kernels”, Studia Mathematica 267 (2) (2022), 121-160, doi: 10.4064/sm210823-10-3 [ PDF: English, arXiv: 1904.13371]
  6. C. Cuenca, G. Olshanski, “Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions”, Adv. in Mathematics, 395 (2022), 108087, ISSN 0001-8708, doi.org/10.1016/j.aim.2021.108087 [ PDF: English, arXiv: 2102.01947]
  7. G. Olshanski, "The centralizer construction and Yangian-type algebras" [ PDF: English, arXiv: 2208.04809]
  8. G. Olshanski, “Macdonald polynomials and extended Gelfand–Tsetlin graph” Sel. Math. New Ser. 27, 41 (2021), doi.org/10.1007/s00029-021-00660-3, [ PDF: English, arXiv: 2007.06261]
  9. G. Olshanski, “Macdonald-level extension of beta ensembles and large-N limit transition”, Commun. Math. Phys. 385 (2021), 595-631, doi.org/10.1007/s00220-020-03899-7 [ PDF: English, arXiv: 2007.06264]
  10. C. Cuenca, V. Gorin, G. Olshanski, “The Elliptic Tail Kernel” International Mathematics Research Notices. Vol. 2021, No. 19, pp. 14922-14964, https://doi.org/10.1093/imrn/rnaa038 [ PDF: English, arXiv: 1907.11841]
  11. C. Cuenca, G. Olshanski, “Elements of the q-Askey scheme in the algebra of symmetric functions”, Moscow Mathematical Journal, 20 (2020), no.4, 50 pp. [ PDF: English, arXiv: 1808.06179 ]
  12. G. Olshanski, “Determinantal point processes and fermion quasifree states”, Commun. Math. Phys. 378 (2020), 507-555; doi.org/10.1007/s00220-020-03716-1 [ PDF: English, arXiv: 2002.10723]
  13. G. Olshanski, “The topological support of the z-measures on the Thoma simplex”, Functional Analysis and its Applications 52:4 (2018), 308–310, [ PDF: English, arXiv: 1809.07125]
  14. G. Olshanski, “Interpolation Macdonald polynomials and Cauchy-type identities”, J. Combin. Theory Ser. A 162 (2019), 65-117 [ PDF: English, arXiv: 1712.08018 ]
  15. A. Borodin, G. Olshanski, “The ASEP and determinantal point processes”, Com- munications in Mathematical Physics 353 (2017), 853–903, [ PDF: English, arXiv: 1608.01564 ]
  16. Г.И. Ольшанский, “Аналог больших полиномов q-Якоби в алгебре симметрических функций / An analogue of the big q-Jacobi polynomials in the algebra of symmetric functions”, Функц. анализ и его прил., 51:3 (2017), 56–76, Functional Analysis and its Applications 51:3 (2017), 204–220 [ PDF: English, arXiv: 1705.06543 ]
  17. G. Olshanski, A. Borodin, “Representations of the infinite symmetric group”. Cambridge University Press, 2017.
  18. Г. И. Ольшанский, “Диффузионные процессы на конусе Тома / Diffusion processes on the Thoma cone”, Функц. анализ и его прил., 50:3 (2016), 85–90, Functional Analysis and its Appli- cations 50 (2016), 237–240
  19. Г. И. Ольшанский, “Расширенный граф Гельфанда–Цетлина, его q-граница и q-B-сплайны / Extended Gelfand–Tsetlin graph, its q-boundary, and q-B-splines”, Функц. анализ и его прил., 50:2 (2016), 31–60, Functional Analysis and its Applications 50 (2016), no. 2, 107–130 [ PDF: English, arXiv: 1607.04201 ]
  20. V. Gorin, G. Olshanski, “A quantization of the harmonic analysis on the infinite-dimensional unitary group”, J. of Functional Analysis. 2016. Vol. 270. No. 1. P. 375-418. [ PDF: English, arXiv: 1504.06832 ]
  21. G. Olshanski, “Markov dynamics on the dual object to the infinite-dimensional unitary group”, in: Probability and Statistical Physics in St. Petersburg, vol. 91, pp. 373–394: Proceedings of Symposia in Pure Mathematics. American Mathematical Society, 2016. P. 373-394.
  22. G. Olshanski, “The representation ring of the unitary groups and Markov processes of algebraic origin”, Advances in Mathematics. 2016. Vol. 300. P. 544-615. [ PDF: English, arXiv: 1504.01646 ]
  23. Г. И. Ольшанский, “Аппроксимация марковской динамики на дуальном объекте к бесконечномерной унитарной группе/ Approximation of Markov dynamics on the dual object to the infinite-dimensional unitary group”, Функц. анализ и его прил., 49:4 (2015), 61–75, Functional Analysis and its Applications 49 (2015), 289–300 [ PDF: English, arXiv: 1310.6155 ]
  24. A. Borodin, A. Bufetov, G. Olshanski, “Limit shapes for growing extreme characters of U(∞)”, Annals of Applied Probability. 2015. Vol. 25. No. 4. P. 2339-2381. [ PDF: English, arXiv: 1311.5697 ]
  25. В. Е. Горин, Г. И. Ольшанский, “Детерминантные меры, связанные с большими полиномами q-Якоби / Determinantal measures related to big q-Jacobi poly- nomials”, Функц. анализ и его прил., 49:3 (2015), 70–74, Functional Analysis and its Applications 49 (2015), 214–217
  26. G. Olshanski, A. Osinenko, “Multivariate Jacobi polynomials and the Selberg integral. II”, Теория представлений, динамические системы, комбинаторные методы. XXV, Зап. научн. сем. ПОМИ, 436, ПОМИ, СПб., 2015, 199–218; J. Math. Sci. (N.Y.), 215:6 (2016), 755–768.
  27. A. Borodin, G. Olshanski, “An interacting particle process related to Young tableaux”. Записки научных семинаров ПОМИ. 2014. Vol. 421. P. 47-57, Reproduced in Journal of Mathematical Sciences (New York) 200 (2014), 671-676 [ PDF: English, arXiv: 1303.2795 ]
  28. G. Olshanski, “The Gelfand-Tsetlin graph and Markov processes (invited talk at ICM 2014). In: Proceedings of the International Congress of Mathematicians, Seoul 2014, Vol. IV, pp. 431-453. Seoul, 2014. http://www.icm2014.org/en/vod/proceedings.html, [ PDF: English, arXiv: 1404.3646 ]
  29. A. Borodin, G. Olshanski, “Markov dynamics on the Thoma cone: a model of time-dependent determinantal processes with infinitely many particles”, Electronic Journal of Probability. 2013. Vol. 75. pp. 1-43. [ PDF: English, arXiv: 1303.2794 ]
  30. G. Olshanski, “Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines”, Journal of Lie Theory. 2013. Vol. 23. No. 4. P. 1011-1022. [ PDF: English, arXiv: 1302.7116 ]
  31. E. Lytvynov, G. Olshanski, “Equilibrium Kawasaki dynamics and determinantal point process”, /J. Math. Sci. 2013. Vol.190. No.3. 451-458, doi.org/10.1007/s10958-013-1260-6 [ PDF: English, arXiv: 1210.1362 ]
  32. A. Borodin, G. Olshanski, “The Young bouquet and its boundary”, Mosc. Math. J., 13:2 (2013), 193–232. [ PDF: English, arXiv: 1110.4458 ]
  33. Г. И. Ольшанский, А. Осиненко, “Многомерные многочлены Якоби и интеграл Сельберга/ Multivariate Jacobi polynomials and the Selberg integral”, Функц. анализ и его прил., 46:4 (2012), 31–50, Functional Analysis and its Applications 46 (2012), No. 4, pp. 262–278
  34. A. Borodin, G. Olshanski, “Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary”, Journal of Functional Analysis 263 (2012), 248-303. [ PDF: English, arXiv: 1009.2029 ]
  35. G. Olshanski, “Laguerre and Meixner orthogonal bases in the algebra of symmetric functions”, International Mathematics Research Notices. 2012. Vol. 2012. No. 16. P. 3615-3679. [ PDF: English, arXiv: 1103.5848 ]
  36. A. Borodin, G. Olshanski, “The boundary of the Gelfand-Tsetlin graph: A new approach”, Advances in Mathematics 230 (2012), 1738-1779. [ PDF: English, arXiv: 1109.1412 ]
  37. A. Gnedin, G. Olshanski, “The two-sided infinite extension of the Mallows model for random permutations”, Advances in Applied Mathematics 48 (2012), no. 5, 615-639. [ PDF: English, arXiv: 1103.1498 ]
  38. G. Olshanski, “Random permutations and related topics”, in: The Oxford Handbook on Random Matrix Theory. Oxford : Oxford University Press, 2011. [ PDF: English, arXiv: 1104.1266 ]
  39. G. Olshanski, “The quasi-invariance property for the Gamma kernel determinantal measure”, Advances in Mathematics 226 (2011), 2305-2350. [ PDF: English, arXiv: 0910.0130 ]
  40. G. Olshanski, “Laguerre and Meixner symmetric functions, and infinite-dimensional diffusion processes”, Zapiski Nauchnyh Seminarov POMI 378 (2010), 81-110; Journal of Mathematical Sciences (New York) 174 (2011), no. 1, 41-57. [ PDF: English, arXiv: 1009.2037 ]
  41. G. Olshanski, “Anisotropic Young diagrams and infinite-dimensional diffusion processes with the Jack parameter”, International Mathematics Research Notices 2010 (2010), no.6, 1102-1166. [ PDF: English, arXiv: 0902.3395 ]
  42. A. Gnedin, G. Olshanski, “q-Exchangeability via quasi-invariance”, Annals of Probability 2010, Vol. 38, No. 6, 2103-2135. [ PDF: English, arXiv: 0907.3275 ]
  43. G. Olshanski, “Plancherel averages: Remarks on a paper by Stanley”, Electr. J. Combin. 17 (2010), paper #R43, 16 pp. [ PDF: English, arXiv: 0905.1304 ]
  44. A. Gnedin, G. Olshanski, “A q-analogue of de Finetti’s theorem, Electronic Journal of Combinatorics”, Electronic Journal of Combinatorics 16 (2009), no. 1, paper #R78. [ PDF: English, arXiv: 0905.0367 ]
  45. A. Borodin, G. Olshanski, “Infinite-dimensional diffusions as limits of random walks on partitions”, Prob. Theor. Rel. Fields 144 (2009), no. 1, 281-318. [ PDF: English, arXiv: 0706.1034 ]
  46. Г. И. Ольшанский, “Разностные операторы и детерминантные точечные процессы / Difference operators and determinantal point processes”, Функц. анализ и его прил., 42:4 (2008), 83–97. Func. Anal. Appl. 42 (2008), no. 4, 317-329. [ PDF: English, arXiv: 0810.3751 ]
  47. A. Borodin, G. Olshanski, “Asymptotics of Plancherel-type random partition”, J. Algebra 313 (2007), no. 1, 40-60. [ PDF: English, arXiv: math/0610240 ]
  48. A. Borodin, G. Olshanski, “Meixner polynomials and random partitions”, Mosc. Math. J., 6:4 (2006), 629–655. [ PDF: English, arXiv: math/0609806 ]
  49. A. Gnedin, G. Olshanski, “The boundary of the Eulerian number triangle”, Mosc. Math. J., 6:3 (2006), 461–475. [ PDF: English, arXiv: math/0602610 ]
  50. A. Okounkov, G. Olshanski, “Limits of BC-type orthogonal polynomials as the number of variables goes to infinity”, In: Jack, Hall-Littlewood and Macdonald Polynomials (E.B.Kuznetsov and S.Sahi, eds). Amer. Math. Soc., Contemporary Math. vol. 417, 2006, 281–318 [ PDF: English, arXiv: math/0606085 ]
  51. A. Gnedin, G. Olshanski, “Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams”, Intern. Math. Research Notices 2006, Art. ID 51968, 39 pp. [ PDF: English, arXiv: math/0508131 ]
  52. A. Borodin, G. Olshanski, E. Strahov, “Giambelli compatible point processes”, Adv. in Appl. Math. 37 (2006), no. 2, 209-248. [ PDF: English, arXiv: math-ph/0505021 ]
  53. A. Borodin, G. Olshanski, “Stochastic dynamics related to Plancherel measure on partitions”, Representation Theory, Dynamical Systems, and Asymptotic Combinatorics (V.Kaimanovich and A.Lodkin, eds). Amer. Math. Soc., Translations – Series 2, vol. 217, 2006, 9-22. [ PDF: English, arXiv: math-ph/04020645 ]
  54. A. Borodin, G. Olshanski, “Markov processes on partitions”, Probab. Theory Related Fields 135 (2006), no. 1, 84-152. [ PDF: English, arXiv: math-ph/0409075 ]
  55. A. Borodin, G. Olshanski, “Representation theory and random point processes”, European Congress of Mathematics, Eur. Math. Soc., Zurich, 2005, pp. 73-94. [ PDF: English, arXiv: math/0409333 ]
  56. A. Borodin, G. Olshanski, “Random partitions and the Gamma kernel”, Adv. Math. 194 (2005), no. 1, 141-202. [ PDF: English, arXiv: math-ph/0305043 ]
  57. A. Borodin, G. Olshanski, “Z-measures on partitions and their scaling limits”, European J. Combin. 26 (2005), no. 6, 795-834. [ PDF: English, arXiv: math-ph/0210048 ]
  58. A. Borodin, G. Olshanski, “Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes”, Ann. of Math. 161 (2005), no. 3, 1319-1422. [ PDF: English, arXiv: math/0109194 ]
  59. S, Kerov, G. Olshanski, A. Vershik, “Harmonic analysis on the infinite symmetric group”, Invent. Math. 158 (2004), no. 3, 551-642. [ PDF: English, arXiv: math/0312270 ]
  60. Г. И. Ольшанский, “Вероятностные меры на дуальных объектах к компактным симметрическим пространствам и гипергеометрические тождества / Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities”, Функц. анализ и его прил., 37:4 (2003), 49–73; Funct. Anal. Appl., 37:4 (2003), 281–30.
  61. G. Olshanski, “An introduction to harmonic analysis on the infinite symmetric group”, Asymptotic Combinatorics with Applications to Mathematical Physics (A.M.Vershik, ed.), Springer LNM 1815 (2003), 127-160. [ PDF: English, arXiv: math/0311369 ]
  62. G. Olshanski, “The problem of harmonic analysis on the infinite-dimensional unitary group”, J. Funct. Anal. 205 (2003), no. 2, 464-524. [ PDF: English, arXiv: math/0109193 ]
  63. G. Olshanski, “Point processes and the infinite symmetric group. Part I: The general formalism and the density function”, The orbit method in geometry and physics: in honor of A. A. Kirillov (C. Duval, L. Guieu, V. Ovsienko, eds), Progress in Math. 213. Birkhauser, 2003, pp. 349-393. [ PDF: English, arXiv: math/9804086 ]
  64. G. Olshanski, A. Regev, A. Vershik, “Frobenius-Schur functions”, In: Studies in memory of Issai Schur (Chevaleret/Rehovot, 2000), Progr. Math., vol. 210, Birkhauser Boston, 2003, 251-299. [ PDF: English, arXiv: math/0110077 ]
  65. V. Ivanov, G. Olshanski, “Kerov’s central limit theorem for the Plancherel measure on Young diagrams”, In: S.Fomin, editor. Symmetric Functions 2001: Surveys of Developments and Perspectives (NATO Science Series II. Mathematics, Physics and Chemistry. Vol.74), Kluwer, 2002, pp. 93-151. [ PDF: English, arXiv: math/0304010 ]
  66. A. Borodin, G. Olshanski, “Infinite random matrices and ergodic measures”, Comm. Math. Phys. 223 (2001), no. 1, 87-123. [ PDF: English, arXiv: math-ph/0010015 ]
  67. G. Olshanski, A. Regev, “Random Young Tableaux and Combinatorial Identities”, Seminaire Lotharingien de Combinatoire, 46 (2001), paper B46e. [ PDF: English, arXiv: math/0106074 ]
  68. A. Borodin, G. Olshanski, “Z-Measures on partitions, Robinson–Schensted–Knuth correspondence, and β = 2 ensembles”. In: Random matrix models and their applications (P. M. Bleher and A. R. Its, eds). MSRI Publications, vol. 40, Cambridge Univ. Press, 2001, 71–94 [ PDF: English, arXiv: math/9905189 ]
  69. A. I. Molev, G. I. Olshanski, “Degenerate affine Hecke algebras and centralizer construction for the symmetric groups”, J. Algebra 237 (2001), 302-341. [ PDF: English, arXiv: math/0002165 ]
  70. A. Borodin, G. Olshanski, “Harmonic functions on multiplicative graphs and interpolation polynomials”, Electronic Journal of Combinatorics 7 (2000), paper R28. [ PDF: English, arXiv: math/9912124 ]
  71. A. Molev, G. Olshanski, “Centralizer construction for twisted Yangians”, Selecta Mathematica 6 (2000), no. 3, 269-317. [ PDF: English, arXiv: q-alg/9712050 ]
  72. A. Borodin, A. Okounkov, G. Olshanski, “Asymptotics of Plancherel measures for symmetric groups”, J. Amer. Math. Soc. 13 (2000), no. 3, 481-515. [ PDF: English, arXiv: math/9905032 ]
  73. A. Borodin, G. Olshanski, “Distributions on partitions, point processes, and the hypergeometric kernel”, Commun. Math. Phys. 211 (2000), no. 2, 335-358. [ PDF: English, arXiv: math/9904010 ]
  74. A. Borodin, G. Olshanski, “Point processes and the infinite symmetric group. Part VI: Summary of results”, Math.Res.Lett. 5 (1998) 799-816. [ PDF: English, arXiv: math/9810015 ]
  75. A. Okounkov, G. Olshanski, “Asymptotics of Jack polynomials as the number of variables goes to infinity”, Intern. Math. Research Notices 1998, no. 13, 641-682. [ PDF: English, arXiv: q-alg/9709011 ]
  76. S. Kerov, A. Okounkov, G. Olshanski, “The boundary of Young graph with Jack edge multiplicities”, Intern. Math. Research Notices 1998, no.4, 173-199. [ PDF: English, arXiv: q-alg/9703037 ]
  77. A. Okounkov, G. Olshanski, “Shifted Schur functions II. Binomial formula for characters of classical groups and applications”, Kirillov’s Seminar on Representation Theory. Amer. Math. Soc. Transl. 1998, pp. 245-271. [ PDF: English, arXiv: q-alg/9612025 ]
  78. A. Okounkov, G. Olshanski, “Shifted Jack polynomials, binomial formula, and applications”, Math. Res. Letters, 4 (1997), 69-78. [ PDF: English, arXiv: q-alg/9608020 ]
  79. G. Olshanski, “Generalized symmetrization in enveloping algebras”, Transformation Groups 2 (1997), 197–213.
  80. А. Окуньков, Г. Ольшанский, “Сдвинутые функции Шура / Shifted Schur functions”, Алгебра и анализ, 9:2 (1997), 73–146; St. Petersburg Math. J., 9:2 (1998), 239–300. [ PDF: English, arXiv: q-alg/9605042 ]
  81. Ю. А. Неретин, Г. И. Ольшанский, “Граничные значения голоморфных функций, особые унитарные представления групп O(p,q) и их пределы при q→∞ / Boundary values of holomorphic functions, special unitary representations of the groups O(p, q), and their limits as q→∞”, Теория представлений, динамические системы, комбинаторные и алгоритмические методы. I, Зап. научн. сем. ПОМИ, 223, ПОМИ, СПб., 1995, 9–91; J. Math. Sci. (New York), 87:6 (1997), 3983–4035.
  82. M. Nazarov, G. Olshanski, “Bethe Subalgebras in Twisted Yangians”, Comm. Math. Phys. 178 (1996), 483-506. [ PDF: English, arXiv: q-alg/9507003 ].
  83. G. Olshanski, A. Vershik, “Ergodic unitarily invariant measures on the space of infinite Hermitian matrices”, Contemporary Mathematical Physics. F. A. Berezin’s memorial volume. Amer. Math. Transl. Ser. 2, vol. 175 (R. L. Dobrushin et al., eds), 1996, pp. 137-175. [ PDF: English, arXiv: math/9601215 ]
  84. А. И. Молев, М. Л. Назаров, Г. И. Ольшанский, “Янгианы и классические алгебры Ли / Yangians and classical Lie algebras”, УМН, 51:2(308) (1996), 27–104; Russian Math. Surveys, 51:2 (1996), 205–282.
  85. G. Olshanski, “Cauchy–Szeg ̈o kernels for Hardy spaces on simple Lie groups”, Journal of Lie Theory, 5 (1995), 241–273.
  86. S. Kerov, G. Olshanski, “Polynomial functions on the set of Young diagrams”, Comptes Rendus Acad. Sci. Paris, Ser. I, 319 (1994), 121–126.
  87. Г. И. Ольшанский, “Представление Вейля и нормы гауссовых операторов / Weil representation and norms of Gaussian operators”, Функц. анализ и его прил., 28:1 (1994), 51–67; Funct. Anal. Appl., 28:1 (1994), 42–54.
  88. S. Kerov, G. Olshanski, A. Vershik, “Harmonic analysis on the infinite symmetric group. A deformation of the regular representation”. Comptes Rendus Acad. Sci. Paris. S ́er. 1, 316 (1993), 773-778.
  89. G. Olshanski, “Quantized universal enveloping superalgebra of type Q and a super-extension of the Hecke algebra. Letters in Mathematical Physics 24 (1992), 93-102.
  90. G. Olshanski, “Caract`eres generalis ́es du groupe U(∞) et fonctions interieures”. Comptes Rendus Acad. Sci. Paris. S ́er. 1, 313 (1991), 9–12.
  91. G. Olshanski, “On semigroups related to infinite-dimensional groups”. In: Topics in represen- tation theory (A. A. Kirillov, ed.). Advances in Soviet Math., vol. 2. Amer. Math. Soc., Providence, R.I., 1991, 67-101.
  92. G. Olshanski, “Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians”. In: Topics in Representation Theory (A. A. Kirillov, ed.). Advances in Soviet Math., vol. 2. Amer. Math. Soc., Providence, R.I., 1991, 1-66.
  93. G. Olshanski, “Twisted Yangians and infinite-dimensional classical Lie algebras. CWI Report, Amsterdam, 1991; Lecture Notes in Math. 1510 (1992), 103-120.
  94. G. Olshanski, “Unitary representations of infinite-dimensional pairs (G,K) and the formalism of R. Howe”. In: Representations of Lie groups and related topics. Advances in Contemp. Math., vol. 7 (A. M. Vershik and D. P. Zhelobenko, editors). Gordon and Breach, N.Y., London etc. 1990, 269-463.
  95. M. L. Nazarov, Yu. A. Neretin, G. I. Olshanski, “Semi-groupes engendr’es par la representation de Weil du groupe symplectique de dimension infinie”. Comptes Rendus Acad. Sci. Paris. S ́er. 1, 309, no. 7 (1989), 443-446.
  96. Г. И. Ольшанский, “Унитарные представления (G,K)-пар, связанных с бесконечной симметрической группой S(∞) / Unitary representations of (G, K )-pairs connected with the infinite symmetric group S(∞)”, Алгебра и анализ, 1:4 (1989), 178–209; Leningrad Math. J., 1:4 (1990), 983–1014.
  97. G. Olshanski, “Irreducible unitary representations of the groups U(p,q) sustaining passage to the limit as q → ∞”. Zapiski Nauchn. Semin. LOMI, vol. 172 (1989), 114-120 (Russian); English translation: J. Soviet Math. 59, no. 5 (1992), 1102-1107.
  98. Г. И. Ольшанский, “Метод голоморфных расширений в теории унитарных представлений бесконечномерных классических групп / Method of holomorphic extensions in the representation theory of infinite- dimensional classical groups”, Функц. анализ и его прил., 22:4 (1988), 23–37; Funct. Anal. Appl., 22:4 (1988), 273–285.
  99. Г. И. Ольшанский, “Детерминизм случайных полей Леви и унитарные представления бесконечномерных групп / Determinism of L ́evy random fields and unitary representations of infinite- dimensional groups”, УМН, 43:2(260) (1988), 151–152; Russian Math. Surveys, 43:2 (1988), 183–184.
  100. G. Olshanski, “Extension of the algebra U(g) for infinite-dimensional classical Lie algebras g, and the Yangians Y (gl(m))”. Soviet Math. Dokl. 36, no. 3 (1988), 569-573.
  101. Г. И. Ольшанский, “Янгианы и универсальные обертывающие алгебры / Yangians and universal enveloping algebras”, Дифференциальная геометрия, группы Ли и механика. IX, Зап. научн. сем. ЛОМИ, 164, Изд-во “Наука”, Ленинград. отд., Л., 1987, 142–150. English translation: J. Soviet Math. 47, no. 2 (1989), 2466-2473.
  102. Г. И. Ольшанский, “Унитарные представления группы SO0(∞,∞) как пределы унитарных представлений групп SO0(n,∞) при n→∞ / Unitary representations of the group SO0(∞,∞) as limits of unitary representations of the groups SO0(n,∞) as n→∞”, Функц. анализ и его прил., 20:4 (1986), 46–57; Funct. Anal. Appl., 20:4 (1986), 292–301.
  103. G. Olshanski, “Unitary representations of the infinite symmetric group: a semigroup approach”. In: Representations of Lie groups and Lie algebras (A.A. Kirillov, ed.). Budapest, Akad. Kiado, 1985, 181-198.
  104. G. Olshanski, M. Prati, “Extremal weights of finite-dimensional representations of the Lie superalgebra gln/m”. Il Nuovo Cimento 85A, no. 1 (1985), 1-18.
  105. Г. И. Ольшанский, “Бесконечномерные классические группы конечного R-ранга: описание представлений и асимптотическая теория / Infinite-dimensional classical groups of finite R-rank: description of representations and asymptotic theory”, Функц. анализ и его прил., 18:1 (1984), 28–42; Funct. Anal. Appl., 18:1 (1984), 22–34.
  106. G. Olshanski, “Unitary representations of infinite-dimensional pairs (G, K ) and the formalism of R. Howe”. Soviet Math. Dokl. 27, no. 2 (1983), 290-294.
  107. Г. И. Ольшанский, “Сферические функции и характеры на группе U(∞)X / Spherical functions and characters on the group U(∞)X“, УМН, 37:2(224) (1982), 217–218; Russian Math. Surveys, 37:2 (1982), 233–234.
  108. G. Olshanski, “Complex Lie semigroups, Hardy spaces, and the Gelfand- Gindikin program”. In: Topics in group theory and homological algebra. Yaroslavl University Press, 1982, 85-98 (Russian). English translation: Differential Geometry and its Applications, 1 (1991), 297-308.
  109. G. Olshanski, “Convex cones in symmetric Lie algebras, Lie semigroups, and invariant causal (order) structures on pseudo-Riemannian symmetric spaces”. Soviet Math. Dokl. 26 (1982), 97-101.
  110. Г. И. Ольшанский, “Новые “большие” группы типа I / New “large” groups of type one”, Итоги науки и техн. Сер. Соврем. пробл. мат., 16, ВИНИТИ, М., 1980, 31–52; J. Soviet Math., 18:1 (1982), 22–39.
  111. Г. И. Ольшанский, “Инвариантные упорядочения в простых группах Ли: решение задачи Э. Б. Винберга / Invariant orderings in simple Lie groups: the solution to E.B.Vinberg’s problem”, Функц. анализ и его прил., 16:4 (1982), 80–81; Funct. Anal. Appl., 16:4 (1982), 311–313.
  112. Г. И. Ольшанский, “Инвариантные конусы в алгебрах Ли, полугруппы Ли и голоморфная дискретная серия / Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series”, Функц. анализ и его прил., 15:4 (1981), 53–66; Funct. Anal. Appl., 15:4 (1981), 275–285.
  113. Г. И. Ольшанский, “Описание унитарных представлений со старшим весом для групп U(p,q)˜ / Description of unitary representations with highest weight for the groups U(p,q)˜”, Функц. анализ и его прил., 14:3 (1980), 32–44; Funct. Anal. Appl., 14:3 (1980), 190–200.
  114. G. Olshanski, “Construction of unitary representations of infinite-dimensional classical groups”. Soviet Math. Doklady 21 (1980), 66-70
  115. Г. И. Ольшанский, “Унитарные представления бесконечномерных классических групп U(p,∞), SO0(p,∞), Sp(p,∞) и соответствующих групп движений / Unitary representations of the infinite–dimensional classical groups U(p,∞), SO0(p,∞), Sp(p,∞) and the corresponding motion groups”, Функц. анализ и его прил., 12:3 (1978), 32–44; Funct. Anal. Appl., 12:3 (1978), 185–195.
  116. G. Olshanski, “Unitary representations of the infinite–dimensional classical groups U(p,∞), SO0(p,∞), Sp(p,∞) and the corresponding motion groups. Soviet Math. Doklady 19 (1978), 220-224.
  117. Г. И. Ольшанский, “Классификация неприводимых представлений групп автоморфизмов деревьев Брюа–Титса / Classification of irreducible representations of groups of automorphisms of Bruhat–Tits trees”, Функц. анализ и его прил., 11:1 (1977), 32–42; Funct. Anal. Appl., 11:1 (1977), 26–34.
  118. Г. И. Ольшанский, “О представлениях группы автоморфизмов дерева / On representations of the group of automorphisms of a tree”, УМН, 30:3(183) (1975), 169–170.
  119. Г. И. Ольшанский, “Сплетающие операторы и дополнительные серии в классе представлений полной группы матриц над локально компактной алгеброй с делением, индуцированных с параболических подгрупп”, Матем. сб., 93(135):2 (1974), 218–253; “Intertwining operators and complementary series in the class of representations induced from parabolic subgroups of the general linear group over a locally compact division algebra”, Math. USSR-Sb., 22:2 (1974), 217–255.
  120. Г. И. Ольшанский, “Об унитарных представлениях групп GL(2) и GU(2) над несвязным локально компактным телом кватернионов / On unitary representations of the groups GL(2) and GU(2) over a totally disconnected locally compact quaternion field”, Функц. анализ и его прил., 7:1 (1973), 82–83; Funct. Anal. Appl., 7:1 (1973), 73–75.
  121. Г. И. Ольшанский, “О сплетающих операторах для индуцированных представлений редуктивных p-адических групп / On intertwining operators for induced representations of reductive p-adic groups”, УМН, 27:6(168) (1972), 243–244.
  122. Г. И. Ольшанский, “О теореме двойственности Фробениуса / On the Frobenius reciprocity theorem”, Функц. анализ и его прил., 3:4 (1969), 49–58; Funct. Anal. Appl., 3:4 (1969), 295–302.
  123. Г. И. Ольшанский, “О топологии пространства унитарных представлений нильпотентной группы Ли / Topology of the space of unitary representations of a nilpotent Lie group”, Функц. анализ и его прил., 3:4 (1969), 93–94; Funct. Anal. Appl., 3:4 (1969), 340–342.