报告题目 (Title)：Geometric Howe duality of finite type(有限型几何Howe对偶)
报告人 (Speaker)： 罗栗 教授 (华东师范大学)
报告时间 (Time)：2023年4月23日(周日) 10:00
报告地点 (Place)：F309
邀请人(Inviter)：张红莲、孙建才
报告摘要：We develop a geometric approach toward an interplay between a pair of quantum Schur algebras of arbitrary finite type. Then by Beilinson-Lusztig-MacPherson's stabilization procedure in the setting of partial flag varieties of type A (resp. type B/C), the Howe duality between a pair of quantum general linear groups (resp. a pair of i-quantum groups of type AIII/IV) is established. The Howe duality for quantum general linear groups has been provided via quantum coordinate algebras.
We also generalize this algebraic approach to i-quantum groups of type AIII/IV, and prove that the quantum Howe duality derived from partial flag varieties coincides with the one constructed by quantum coordinate (co)algebras. Moreover, the explicit multiplicity-free decompositions for these Howe dualities are obtained.