Affine walled Brauer-Clifford superalgebras

JOURNAL OF ALGEBRA

卷:525

Article

Gao, Mengmeng¹  Rui, Hebing¹  Song, Linliang¹  Su, Yucai¹ 

[1] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

关键词: Affine walled Brauer-Clifford superalgebras;    Queer Lie superalgebra;    Schur-Weyl duality;   

DOI  :  10.1016/j.jalgebra.2019.01.014

来源: Elsevier

【 摘 要 】

In this paper, a notion of affine walled Brauer-Clifford superalgebras BCr,taff is introduced over an arbitrary integral domain R containing 2(-1). These superalgebras can be considered as affinization of walled Brauer superalgebras in [9]. By constructing infinitely many homomorphisms from BCr,taff to a class of level two walled Brauer-Clifford superalgebras over C, we prove that BCr,taff is free over R with infinite rank. We explain that any finite dimensional irreducible BCr,taff-module over an algebraically closed field F of characteristic not 2 factors through a cyclotomic quotient of BC,1, called a cyclotomic (or level k) walled Brauer-Clifford superalgebra BCk,r,t. Using a previous method on cyclotomic walled Brauer algebras in [15], we prove that BCk,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 in the sense of Definition 6.4. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free