On u-deformed Kottwitz's involution modules

Title: On u-deformed Kottwitz's involution modules

报告人：胡峻 教授（北京理工大学）

地点：玉泉校区工商楼105

摘要: Let (W,S) be a Coxeter system and $/ast$ an automorphism of W with order $/leq 2$ and $S^{/ast}=S$.
Lusztig and Vogan have introduced a u-deformed version $M_u$ of Kottwitz's involution module over the Iwahori--Hecke algebra $H_{u}(W)$ with Hecke parameter $u^2$. Lusztig has conjectured that $M_u$ is isomorphic to the left ideal of $H_{u}(W)$ generated by $/sum_{w^*=w/in W}u^{-/ell(w)}T_w$. In this talk I will present some recent progress on this conjecture and its generalization to more general ground base ring.