|
September 11, 2023 / Vadim Vologodsky (HSE Univ.) = = Arithmetic of the Knizhnik-Zamolodchikov equation September 25, 2023 / Evgeny Anikin (Russian Quantum Center) = = Entangling gate fidelities in trapped ion quantum computers: perturbative calculations October 2, 2023 / Michael Finkelberg (Skoltech, HSE Univ., IITP) = = Cherkis-Nakajima-Takayama bow varieties October 9, 2023 / zoom / Andrey Losev (Univ. of Science and Technology of China, HSE Univ.) = = On beta-functions in first order theories October 23, 2023 / Aleksandr Artemev (Skoltech, Landau Inst.) = = (2,2p+1) minimal string, moduli space volumes, and classical Liouville theory October 30, 2023 / Anton Il’yn (Lebedev Inst., HSE Univ.) = = Geometry of isotropic stochastic flows November 13, 2023 / Filipp Uvarov (HSE Univ.) = = Deligne’s category, monodromy-free pseudo-differential operators, and Gaudin model associated with the super Lie algebra gl(m|n) (1/2) November 20, 2023 / Alexander Belalvin (Landau Inst.) = = Mirror symmetry and a new approach to constructing orbifolds of Gepner models November 27, 2023 / Filipp Uvarov (HSE Univ.) = = Deligne’s category, monodromy-free pseudo-differential operators, and Gaudin model associated with the super Lie algebra gl(m|n) (2/2) |
December 4, 2023
Michel Semenov-Tian-Shansky
Let $\mathfrak g$ be a semisimple Lie algebra and $\mathfrak g = \mathfrak n \oplus \mathfrak h \oplus \mathfrak n_-$ a triangular decomposition. Motivated by a construction of Kostant-Lipsman-Wolf, we construct an integrable system on the dual space of $\mathfrak n_-$ equipped with the Kirillov-Kostant Poisson structure. The Bott-Samelson coordinates on the open Bruhat cell (equipped with the standard Poisson structure) makes it into a symmetric Poisson CGL extension, hence giving rise to a $T$-Poisson cluster structure on it. Our integrable system is obtained from the initial cluster by taking the lowest degree terms of the initial cluster variables. We conjecture that mutation of clusters gives rise to mutation of integrable systems. This is joint work in progress with Yanpeng Li and Jiang-Hua Lu