USTC Mathematical Physics (Integrable systems) Seminar—— Poisson-Lie dual of semisimple groups and cluster algebras
发文时间：2020-06-04
来源：304am永利集团
Speaker: Linhui Shen, Michigan State University
Time: Thursday 9:00-10:30 (Beijing Time), June 4, 2020
Zoom (725-874-7880, 314159)
Abstract: Let $G$ be a complex connected semisimple group with the standard Poisson-Lie structure and let $G^\ast$ be its dual Poisson-Lie group. The coordinate ring $\mathcal{O}(G^\ast)$ is a Poisson algebra whose deformation quantization gives rise to the quantum group $\mathcal{U}_q(\mathfrak{g})$. We embed $\mathcal{O}(\G^\ast)$ into a larger cluster Poisson algebra together with a Weyl group action. By applying bases theory of cluster algebras, we obtain a natural linear basis $\Theta$ of $\mathcal{O}(\G^\ast)$ with positive integer structure coefficients. We show that the basis $\Theta$, as a set, is invariant under Lusztig's braid group action.
