Geometric Howe dualities of finite type

发布时间：2021-10-13 作者：浏览次数：

Speaker:	罗栗	DateTime:	2021年10月28日(周四)下午1：30-2：30
Brief Introduction to Speaker: 罗栗，副教授，博导，博士毕业于中国科学院数学与系统科学研究院，现任职于华东师范大学数学科学学院。主要从事量子代数及其典范基实现、李超代数特征标等表示论方向的研究。论文发表于 Mem. Amer. Math. Soc., J. Int. Math. Jussieu, Transform. Groups, IMRN, JLMS 等多个国际重要数学期刊上。目前主持国家自然科学基金面上项目。		Place:	腾讯会议，会议号请联系常浩老师
Abstract: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. This is joint work with Zheming Xu.

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