Affine Periplectic Brauer Algebras

Abstract

We formulate Nazarov-Wenzl type algebras ${\hat{P}}_d^{-}$ for the representation theory of the Periplectic Lie superalgebras $\mathfrak{p}(n)$. We establish a Arakawa-Suzuki type theorem to provide a connection between $\mathfrak{p}(n)$-representations and ${\hat{P}}_d^{-}$-representations. We also consider various tensor product representations for ${\hat{P}}_d^{-}$. The periplectic Brauer algebra $A_d$ defined by Moon is an quotient of ${\hat{P}}_d^{-}$. In particular, actions induced by Jucys-Murphy elements can be obtained under the tensor product representation of ${\hat{P}}_d^{-}$. Also, a Poincare-Birkhoff-Witt type basis for ${\hat{P}}_d^{-}$ is obtained.

23 pages

References in corpus (2)

• On representations of the Lie superalgebra p(n)
• The marked Brauer category