Vol. 16, No. 4, 2022

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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
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 𝔬𝔰𝔭(1|2)(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