Supercharacters of queer Lie superalgebras

Abstract

Let $\mathfrak{g}={\mathfrak{g}}_{\bar{0}}\oplus {\mathfrak{g}}_{\bar{1}}$ be the queer Lie superalgebra and let $L$ be a finite-dimensional non-trivial irreducible $\mathfrak{g}$-module. Restricting the $\mathfrak{g}$-action on $L$ to ${\mathfrak{g}}_{\bar{0}}$, we show that the space of ${\mathfrak{g}}_{\bar{0}}$-invariants $L^{{\mathfrak{g}}_{\bar{0}}}$ is trivial. As a consequence we establish a conjecture first formulated by Gorelik, Grantcharov and Mazorchuk on the triviality of the supercharacter of irreducible $\mathfrak{g}$-modules in the case when the modules are finite dimensional.

12 pages

References in corpus (2)

• Finite-dimensional half-integer weight modules over queer Lie superalgebras
• Character formulae for queer Lie superalgebras and canonical bases of types $A/C$

Cited by in corpus (3)

• Bipartite extension graphs and the Duflo--Serganova functor
• Candidate for the crystal $B(-\infty )$ for the queer Lie superalgebra
• On the Grothendieck ring of a quasireductive Lie superalgebra