The affine VW supercategory.

We define the affine VW supercategory , which arises from studying the action of the periplectic Lie superalgebra p (n) on the tensor product M ⊗ V ⊗ a of an arbitrary representation M with several copies of the vector representation V of p (n) . It plays a role analogous to that of the degenerate affine Hecke algebras in the context of representations of the general linear group; the main obstacle was the lack of a quadratic Casimir element in p (n) ⊗ p (n) . When M is the trivial representation, the action factors through the Brauer supercategory s B r . Our main result is an explicit basis theorem for the morphism spaces of and, as a consequence, of s B r . The proof utilises the close connection with the representation theory of p (n) . As an application we explicitly describe the centre of all endomorphism algebras, and show that it behaves well under the passage to the associated graded and under deformation. [ABSTRACT FROM AUTHOR]