数学学科Seminar第2366讲 有限型几何Howe对偶

创建时间:  2023/04/23  龚惠英   浏览次数: 221   返回

报告题目 (Title):有限型几何Howe对偶(Geometric Howe duality of finite type)

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):校本部F309

邀请人(Inviter):张红莲、孙建才

主办部门:理学院数学系

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.

上一条:数学学科Seminar第2367讲 乘法条件下正则基的正性

下一条:上海大学核心数学研究所——几何与分析综合报告第30讲 Eta不变量的两个应用


数学学科Seminar第2366讲 有限型几何Howe对偶

创建时间:  2023/04/23  龚惠英   浏览次数: 221   返回

报告题目 (Title):有限型几何Howe对偶(Geometric Howe duality of finite type)

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):校本部F309

邀请人(Inviter):张红莲、孙建才

主办部门:理学院数学系

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.

上一条:数学学科Seminar第2367讲 乘法条件下正则基的正性

下一条:上海大学核心数学研究所——几何与分析综合报告第30讲 Eta不变量的两个应用