Affine walled Brauer–Clifford superalgebras.

Abstract In this paper, a notion of affine walled Brauer–Clifford superalgebras B C r , t aff 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 B C r , t aff to a class of level two walled Brauer–Clifford superalgebras over C , we prove that B C r , t aff is free over R with infinite rank. We explain that any finite dimensional irreducible B C r , t aff -module over an algebraically closed field F of characteristic not 2 factors through a cyclotomic quotient of B C r , t aff , called a cyclotomic (or level k) walled Brauer–Clifford superalgebra B C k , r , t. Using a previous method on cyclotomic walled Brauer algebras in [15] , we prove that B C 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 in the sense of Definition 6.4. [ABSTRACT FROM AUTHOR]