On the Grothendieck ring of a quasireductive Lie superalgebra

Abstract

Given a Lie superalgebra $\mathfrak{g}$ and a maximal quasitoral subalgebra $\mathfrak{h}$, we consider properties of restrictions of $\mathfrak{g}$-modules to $\mathfrak{h}$. This is a natural generalization of the study of characters in the case when $\mathfrak{h}$ is an even maximal torus. We study the case of $\mathfrak{g}={\mathfrak{q}}_n$ with $\mathfrak{h}$ a Cartan subalgebra, and prove several special properties of the restriction in this case, including an explicit realization of the $\mathfrak{h}$-supercharacter ring.

fixed typos; to appear in Algebra & Number Theory

References in corpus (2)

• Jacobson-Morozov Lemma for Algebraic Supergroups
• Extension Quiver for Lie Superalgebra $\mathfrak{q}(3)$