Affine walled Brauer algebras

Abstract

A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commutative ring containing 1. Then level two walled Brauer algebras over C are defined, which are some cyclotomic quotients of affine walled Brauer algebras. We establish a super Schur-Weyl duality between affine walled Brauer algebras and general linear Lie superalgebras, and realize level two walled Brauer algebras as endomorphism algebras of tensor modules of Kac modules with mixed tensor products of the natural module and its dual over general linear Lie superalgebras, under some conditions. We also prove the weakly cellularity of level two walled Brauer algebras, and give a classification of their irreducible modules over C. This in tur enables us to classify the indecomposable direct summands of the said tensor modules.

LaTeX, 35 pages

References in corpus (2)

• Cellularity of Cyclotomic Birman--Wenzl--Murakami algebras
• Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras

Cited by in corpus (6)

• First fundamental theorems of invariant theory for quantum supergroups
• A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
• The first fundamental theorem of invariant theory for the orthosymplectic super group
• The degenerate affine walled Brauer algebra
• Supersymmetric polynomials and the center of the walled Brauer algebra
• Highest weight vectors of mixed tensor products of general linear Lie superalgebras