题 目：Affine walled Brauer-Clifford superalgebras

报告人：苏育才 教授，博士生导师，同济大学数学科学学院

时 间：2017年11月17日（周五）下午 15：30

地 点：数学院A302

主 办：数学学院

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报告人及报告内容简介：

苏育才，同济大学特聘教授，博士生导师，数学所所长。国务院政府特殊津贴获得者，国家杰出青年基金获得者，中国科学院****获得者，教育部跨世纪优秀人才。主持多项国家自然科学基金重点项目和面上项目。主要研究领域包括代数学中的李理论、数学物理中的共形场论、理论物理中的超对称性等。在Adv.Math., J.Eur.Math.Soc., Proc.London.Math.Soc., Comm.Math.Phys., Israel J.Math., Math.Z.等刊物发表SCI论文一百余篇。

Abstract:A notion ofaffine walled Brauer-Clifford superalgebras $BC_{r,t}^{\rm aff}$ is introduced over an arbitrary integral domain $R$ containing $2^{-1}$. These superalgebras can be considered asaffinization of walled Brauer superalgebras.By constructing infinite many homomorphisms from $BC_{r,t}^{\rm aff}$ to a class of level two walled Brauer-Clifford superagebras over$\mathbb C$, we provethat$BC_{r,t}^{\rm aff}$ is free over $R$ with infinite rank. We explainthat any finite dimensional irreducible$BC_{r,t}^{\rm aff}$-module over an algebraically closed field $F$ of characteristic not $2$factors through a cyclotomic quotient of$BC_{r,t}^{\rm aff}$, calledacyclotomic(or level $k$)walled Brauer-Clifford superalgebra$BC_{k,r,t}$. Using a previous method on cyclotomic walled Brauer algebras, we provethat $BC_{k,r,t}$isfree over $R$ withsuper rank $(k^{r+t}2^{r+t-1}(r+t)!, k^{r+t}2^{r+t-1} (r+t)!)$ if and only ifit is admissible. Finally, we prove that the degenerate affine (resp., cyclotomic)walled Brauer-Clifford superalgebras defined by Comes-Kujawa areisomorphic to our affine (resp., cyclotomic)walled Brauer-Clifford superalgebras. This is a joint work with Mengmeng Gao, Hebing Rui and Linliang Song.