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报告题目: Representations of cyclotomic Brauer categories and Kauffman categories

报 告 人: 宋林亮 副教授 (同济大学)

报告时间: 2021年05月19日（星期三）下午14:30-15:30

报告地点：腾讯会议 会议号: 614906259 会议密码: 210519

邀 请 人: 常智华 副教授

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数学学院

 2021年05月18日

报告摘要：

Brauer category and Kauffman category are category versions of Brauer algebras and BMW algebras, respectively.  Let $A$ be the locally unital algebra associated to (cyclotomic) Brauer categories or Kauffman categories. We prove that the category $A$-lfdmod of locally finite dimensional left $A$-modules is an upper finite fully stratified category in the sense of Brundan-Stroppel.  It is an upper finite highest weight category if the (degenerate) cyclotomic Hecke algebras are semisimple. Moreover, $A$ is semisimple if and only if its centralizer subalgebras associated to certain idempotent elements are semisimple.  Furthermore, certain endofunctors are defined and give categorical actions of some Lie algebras on the subcategory of $A$-lfdmod consisting of all objects which have a finite standard filtration. This leads to categorifications of certain representations of the classical limits of coideal algebras. This talk is based on joint works with Hebing Rui, Mengmeng Gao.