Affine periplectic Brauer algebras

We formulate Nazarov–Wenzl type algebras Pˆ_d ⁻ 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 Pˆ_d ⁻-representations. We also consider various tensor product representations for Pˆ_d ⁻. The periplectic Brauer algebra A_d developed by Moon is a quotient of Pˆ_d ⁻. In particular, actions induced by Jucys–Murphy elements can also be recovered under the tensor product representation of Pˆ_d ⁻. Moreover, a Poincare–Birkhoff–Witt type basis for Pˆ_d ⁻ is obtained. A diagram realization of Pˆ_d ⁻ is also obtained.