Abstract

The periplectic Lie superalgebra p(n) is a superanalogue of the orthogonal or symplectic Lie algebra preserving an odd non-degenerate symmetric or skew-symmetric bilinear form. Moon used generator and relation to define the periplectic Brauer algebra, which can be used to describe the endomorphism algebra of tensor power of natural representations of p(n). Recently, Kujawa and Tharp gave diagrammatic description of this algebra.

In this talk, we will first recall Moon's Schur-Weyl duality for p(n). We will formulate a degenerate affine version of periplectic Brauer algebra including its diagram interpretation. This is a joint work with Yung-Ning Peng.