Lusztig sheaves and integrable highest weight modules
数学专题报告
报告题目(Title)：Lusztig sheaves and integrable highest weight modules
报告人(Speaker)：兰亦心（中国科学院数学与系统科学研究院）
地点(Place)：后主楼1223
时间(Time)：2023年11月14日 16:00-16:50
邀请人(Inviter)：肖杰
报告摘要
We consider the localization $Q_{V,W}/N_V$ of Lusztig's sheaves for framed quivers, and define functors $E_i^{(n)},F_i^{(n)},K_i^{\pm}$ between the localizations. With these functors, the Grothendieck group of localizations realizes the irreducible integrable highest weight modules $L(\Lambda)$ of quantum groups. Moreover, the nonzero simple perverse sheaves in localizations form the canonical bases of $L(\Lambda)$. We also compare our realization (at $v \rightarrow 1$) with Nakajima's realization via quiver varieties and prove that the transition matrix between canonical bases and fundamental classes is upper triangular with diagonal entries all equal to $\pm 1$.
