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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2409.09255 |
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| _version_ | 1866917778942853120 |
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| author | DeBacker, Stephen Haley, Jacob |
| author_facet | DeBacker, Stephen Haley, Jacob |
| contents | Suppose $\mathfrak{g}$ is a semisimple complex Lie algebra and $\mathfrak{h}$ is a Cartan subalgebra of $\mathfrak{g}$. To the pair $(\mathfrak{g},\mathfrak{h})$ one can associate both a Weyl group and a set of Kac diagrams. There is a natural map from the set of elliptic conjugacy classes in the Weyl group to the set of Kac diagrams. In both this setting and the twisted setting, this paper (a) shows that this map is injective and (b) explicitly describes this map's image. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kac Diagrams for Elliptic Weyl Group Elements DeBacker, Stephen Haley, Jacob Representation Theory Primary 20G07, Secondary 20F55, 20E45 Suppose $\mathfrak{g}$ is a semisimple complex Lie algebra and $\mathfrak{h}$ is a Cartan subalgebra of $\mathfrak{g}$. To the pair $(\mathfrak{g},\mathfrak{h})$ one can associate both a Weyl group and a set of Kac diagrams. There is a natural map from the set of elliptic conjugacy classes in the Weyl group to the set of Kac diagrams. In both this setting and the twisted setting, this paper (a) shows that this map is injective and (b) explicitly describes this map's image. |
| title | Kac Diagrams for Elliptic Weyl Group Elements |
| topic | Representation Theory Primary 20G07, Secondary 20F55, 20E45 |
| url | https://arxiv.org/abs/2409.09255 |