Integrable systems on the dual of nilpotent Lie subalgebras and $T$-Poisson cluster structures
发布时间：2023年12月15日
浏览次数：1515
发布者: Wenqiong Li
主讲人： Yu Li (University of Toronto)
活动时间： 从 2023-12-19 14:00 到 15:00
场地： Room 29, Quan Zhai, BICMR
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.
