The Grothendieck ring of the periplectic Lie supergroup and supersymmetric functions

Abstract

We show that the Grothendieck ring of finite-dimensional representations of the periplectic Lie supergroup $P(n)$ is isomorphic to the ring of symmetric polynomials in $x_1^{\pm 1},\dots ,x_n^{\pm 1}$ whose evaluation $x_1=x_2^{-1}=t$ is independent of $t$.

9 pages, submitted. arXiv admin note: substantial text overlap with arXiv:1906.01948