The periplectic Lie superalgebra from a diagrammatic perspective

One approach to the study of the representation theory of the general linear Lie algebra is to look at the endomorphism algebras of tensor powers of the vector representation and of bigger tensor products with more general representations. The classical and higher Schur-Weyl dualities relate these algebras to the symmetric group and the degenerate affine Hecke algebra respectively, and have been subsequently generalized to other types, such as the symplectic and special orthogonal Lie algebras. We study the periplectic Lie superalgebra p(n) and define diagrammatically the affine VW supercategory sVW, which generalizes the Brauer supercategory and maps to the category of p(n)-representations. This functor allows us to obtain a basis for the morphism spaces of sVW as well as study the representation theory of p(n).