Mathematical Research Letters

Volume 28 (2021)

Number 4

Grothendieck rings of periplectic Lie superalgebras

Pages: 1175 – 1195

DOI:  https://dx.doi.org/10.4310/MRL.2021.v28.n4.a8

Authors

Mee Seong Im (Dept. of Mathematical Sciences, United States Military Academy, West Point, New York, U.S.A.; and Dept. of Mathematical Sciences, United States Naval Academy, Annapolis, Maryland, U.S.A.)

Shifra Reif (Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel)

Vera Serganova (Department of Mathematics, University of California, Berkeley, Calif., U.S.A.)

Abstract

We describe explicitly the Grothendieck rings of finite-dimensional representations of the periplectic Lie superalgebras. In particular, the Grothendieck ring of the Lie supergroup $P(n)$ is isomorphic to the ring of symmetric polynomials in $x^{\pm 1}_{1} , \dotsc , x^{\pm 1}_{n}$ whose evaluation $x_1 = x^{-1}_{2} = t$ is independent of $t$.

This project is partially supported by ISF Grant No. 1221/17, NSF grant 1701532, and United States Military Academy’s Faculty Research Fund.

Received 20 August 2019

Accepted 3 May 2020

Published 22 November 2021