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Affine walled BrauerClifford superalgebras
宋林亮(同济大学)
Thursday, October 19th, 2017, 3:30 PM 数学系126室 

摘要：In this talk, a notion of affine walled BrauerClifford 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 which are introduced by Jung and Kang. By constructing infinite many homomorphisms from $BC_{r, t}^{\rm aff}$ to a class of level two walled BrauerClifford 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 BrauerClifford 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 $(k^{r+t}2^{r+t1} (r+t)!, k^{r+t}2^{r+t1} (r+t)!)$ if and only if it is admissible. Finally, we prove that the degenerate affine walled BrauerClifford superalgebras defined by Comes and Kujawa are isomorphic to our affine walled BrauerClifford superalgebras.
This is a joint work with Mengmeng Gao, Hebing Rui and Yucai Su.



