Spherical supervarieties
[Supervariétés sphériques]
Annales de l'Institut Fourier, Online first, 44 p.

Nous introduisons les supervariétés sphériques, une généralisation des variétés sphériques. Nous prouvons une caractérisation des supervariétés sphériques affines qui généralise une caractérisation classique des variétés sphériques affines. De plus, nous montrons quelques propriétés du monoïde des plus grands poids. Nous discutons plusieurs exemples intéressants qui montrent des différences avec le cas classique parmi lesquels la représentation régulière, les supervariétés symétriques, et les actions de super groupes gradués.

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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DOI : https://doi.org/10.5802/aif.3421
Classification : 17B05,  17B10,  14M27
Mots clés : superalgèbres de Lie, variétés sphériques
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Sherman, Alexander. Spherical supervarieties. Annales de l'Institut Fourier, Online first, 44 p.

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