Affine walled Brauer-Clifford superalgebras


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:20171117日(周五)下午 1530

地  点:数学院A302

主  办:数学学院



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,中国科学院百人计划获得者,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 of affine 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 as affinization 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 prove that $BC_{r,t}^{\rm aff}$ is free over $R$ with infinite rank. We explain that 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 $BC_{r,t}^{\rm aff}$, called a cyclotomic (or level $k$) walled Brauer-Clifford superalgebra $BC_{k,r,t}$. Using a previous method on cyclotomic walled Brauer algebras, we prove that $BC_{k,r,t}$ is free over $R$ with super rank $(k^{r+t}2^{r+t-1}(r+t)!, k^{r+t}2^{r+t-1} (r+t)!)$ if and only if it is admissible. Finally, we prove that the degenerate affine (resp., cyclotomic) walled Brauer-Clifford superalgebras defined by Comes-Kujawa are isomorphic to our affine (resp., cyclotomic) walled Brauer-Clifford superalgebras. This is a joint work with Mengmeng Gao, Hebing Rui and Linliang Song.