Snowflake modules and Enright functor for Kac–Moody superalgebras

Gorelik, Maria; Serganova, Vera

doi:10.2140/ant.2022.16.839

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Snowflake modules and Enright functor for Kac–Moody superalgebras

Maria Gorelik and Vera Serganova

Vol. 16 (2022), No. 4, 839–879

DOI: 10.2140/ant.2022.16.839

Abstract

We introduce a class of modules over Kac–Moody superalgebras; we call these modules snowflake modules. These modules are characterized by invariance property of their characters with respect to a certain subgroup of the Weyl group. Examples of snowflake modules appear as admissible modules in representation theory of affine vertex algebras and in the classification of bounded weight modules. Using these modules we prove Arakawa’s theorem for the Lie superalgebra $𝔬 𝔰 𝔭 {(1 | 2 ℓ)}^{(1)}$ .

Keywords

Kac–Moody superalgebra, Enright functor

Mathematical Subject Classification

Primary: 17B10

Milestones

Received: 19 August 2019

Revised: 18 March 2021

Accepted: 13 June 2021

Published: 5 August 2022

Authors

Maria Gorelik
Department of Mathematics Weizmann Institute of Science Rehovot Israel

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

Vol. 16, No. 4, 2022