On Jordan classes for Vinberg's theta-groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866910644539752448 |
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| author | Carnovale, Giovanna Esposito, Francesco Santi, Andrea |
| author_facet | Carnovale, Giovanna Esposito, Francesco Santi, Andrea |
| contents | Popov has recently introduced an analogue of Jordan classes (packets, or decomposition classes) for the action of a theta-group (G_0,V), showing that they are finitely-many, locally-closed, irreducible unions of G_0-orbits of constant dimension partitioning V. We carry out a local study of their closures showing that Jordan classes are smooth and that their closure is a union of Jordan classes. We parametrize Jordan classes and G_0-orbits in a given class in terms of the action of subgroups of Vinberg's little Weyl group, and include several examples and counterexamples underlying the differences with the symmetric case and the critical issues arising in the theta-situation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_02173 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On Jordan classes for Vinberg's theta-groups Carnovale, Giovanna Esposito, Francesco Santi, Andrea Representation Theory Algebraic Geometry 17B70, 17B45, 20G05 Popov has recently introduced an analogue of Jordan classes (packets, or decomposition classes) for the action of a theta-group (G_0,V), showing that they are finitely-many, locally-closed, irreducible unions of G_0-orbits of constant dimension partitioning V. We carry out a local study of their closures showing that Jordan classes are smooth and that their closure is a union of Jordan classes. We parametrize Jordan classes and G_0-orbits in a given class in terms of the action of subgroups of Vinberg's little Weyl group, and include several examples and counterexamples underlying the differences with the symmetric case and the critical issues arising in the theta-situation. |
| title | On Jordan classes for Vinberg's theta-groups |
| topic | Representation Theory Algebraic Geometry 17B70, 17B45, 20G05 |
| url | https://arxiv.org/abs/2007.02173 |