On the Grothendieck ring of a quasireductive Lie superalgebra

Gorelik, Maria; Serganova, Vera; Sherman, Alexander

doi:10.2140/ant.2025.19.2369

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On the Grothendieck ring of a quasireductive Lie superalgebra

Maria Gorelik, Vera Serganova and Alexander Sherman

Vol. 19 (2025), No. 12, 2369–2407

DOI: 10.2140/ant.2025.19.2369

Abstract

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

Keywords

Lie superalgebra, Duflo–Serganova functor, queer superalgebra, representation theory, Grothendieck group

Mathematical Subject Classification

Primary: 17B10, 17B20, 17B55, 17D10

Milestones

Received: 7 September 2023

Revised: 8 November 2024

Accepted: 23 December 2024

Published: 20 October 2025

Authors

Maria Gorelik
Department of Mathematics Weizmann Institute of science 76100 Rehovot Israel

Vera Serganova
Department of Mathematics University of California Berkeley, CA 94720-3840 United States

Alexander Sherman
School of Mathematics and Statistics University of Sydney Camperdown NSW 2050 Australia

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Vol. 19, No. 12, 2025