Spherical supervarieties

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 15 Mar 2022Embargo end date: 01 Jan 2019 English Publisher:MathDoc/Centre MersenneJournal:Annales de l'Institut Fourier, volume 71, pages 1,449-1,492 (eissn: 1777-5310,

Copyright policy )Funded by:NSF | Large Non-Semisimple Cate...

Authors: Sherman, Alexander;

doi: 10.5802/aif.3421 , 10.48550/arxiv.1910.09610

arXiv: 1910.09610

Spherical supervarieties

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Abstract

We give a definition of the notion of spherical varieties in the world of complex supervarieties with actions of algebraic supergroups. A characterization of affine spherical supervarieties is given which generalizes a characterization in the classical case. We also explain some general properties of the monoid of highest weights. Several examples are discussed that are interesting in their own right and highlight differences with the classical case, including the regular representation, symmetric supervarieties, and actions of graded supergroups.

Related Organizations

University of California, Berkeley
United States

Keywords

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), FOS: Mathematics, Compactifications; symmetric and spherical varieties, Structure theory for Lie algebras and superalgebras, Lie superalgebras, spherical varieties, Representation Theory (math.RT), Mathematics - Representation Theory

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