SPHERICAL SUPERVARIETIES

Alexander Sherman

doi:10.5802/aif.3421

SPHERICAL SUPERVARIETIES

Alexander Sherman

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English
Pages (from-to)	1449-1492
Number of pages	44
Journal	Annales de l'Institut Fourier
Volume	71
Issue number	4
DOIs	https://doi.org/10.5802/aif.3421
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

Lie superalgebras
spherical varieties

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.5802/aif.3421

Cite this

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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.",

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AB - 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.

KW - Lie superalgebras

KW - spherical varieties

UR - https://www.scopus.com/pages/publications/85132928012

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M3 - Article

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JF - Annales de l'Institut Fourier

IS - 4

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SPHERICAL SUPERVARIETIES

Abstract

Keywords

ASJC Scopus subject areas

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