Grothendieck Rings of Queer Lie Superalgebras

Abstract

We determine the Grothendieck rings of the category of finite-dimensional modules over Queer Lie superalgebras via their rings of characters. In particular, we show that the ring of characters of the Queer Lie supergroup $Q(n)$ is isomorphic to the ring of Laurent polynomials in $x_{1},\ldots,x_{n}$ for which the evaluation $x_{n-1}=-x_{n}=t$ is independent of $t$. We thus complete the description of Grothendieck rings for all classical Lie superalgebras.