Sheaf realization of Bridgeland's Hall algebra of Dynkin type
数学专题报告
报告题目(Title)：Sheaf realization of Bridgeland's Hall algebra of Dynkin type
报告人(Speaker)：方杰鹏（北京大学）
地点(Place)：后主楼1223
时间(Time)：2023年10月10日（周二）15:00-15:50
邀请人(Inviter)：肖杰
报告摘要
Bridgeland realized the whole quantum group U_v(g) via the localization of Ringel-Hall algebra for two-periodic projective complexes of quiver representations over a finite field. We generalize Lusztig's categorical construction and (dual) canonical basis for the nilpotent part U_v(n^+) to Bridgeland's Hall algebra in Dynkin type, and obtain a perverse sheaf realization of global basis for Bridgeland's localizing algebra. In particular, we prove that the dual of canonical basis elements are part of our basis up to powers of v. This is a joint work with Yixin Lan and Jie Xiao.
