Affine periplectic Brauer algebras

Abstract

We formulate Nazarov–Wenzl type algebras Pˆd− for the representation theory of the periplectic Lie superalgebras p(n). We establish an Arakawa–Suzuki type functor to provide a connection between p(n)-representations and Pˆd−-representations. We also consider various tensor product representations for Pˆd−. The periplectic Brauer algebra Ad developed by Moon is a quotient of Pˆd−. In particular, actions induced by Jucys–Murphy elements can also be recovered under the tensor product representation of Pˆd−. Moreover, a Poincare–Birkhoff–Witt type basis for Pˆd− is obtained. A diagram realization of Pˆd− is also obtained.