Convex elements and Steinberg's cross-sections
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914987274928128 |
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| author | Nie, Sian Tan, Panjun Yu, Qingchao |
| author_facet | Nie, Sian Tan, Panjun Yu, Qingchao |
| contents | In this paper, we study convex elements in a (twisted) Weyl group introduced by Ivanov and the first named author. We show that each conjugacy class of the twisted Weyl group contains a convex element, and moreover, the Steinberg cross-sections exist for all convex elements. This result strictly enlarges the cases of Steinberg cross-sections from a new perspective, and will play an essential role in the study of higher Deligne-Lusztig representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex elements and Steinberg's cross-sections Nie, Sian Tan, Panjun Yu, Qingchao Representation Theory Algebraic Geometry Group Theory 20G99, 20F55 In this paper, we study convex elements in a (twisted) Weyl group introduced by Ivanov and the first named author. We show that each conjugacy class of the twisted Weyl group contains a convex element, and moreover, the Steinberg cross-sections exist for all convex elements. This result strictly enlarges the cases of Steinberg cross-sections from a new perspective, and will play an essential role in the study of higher Deligne-Lusztig representations. |
| title | Convex elements and Steinberg's cross-sections |
| topic | Representation Theory Algebraic Geometry Group Theory 20G99, 20F55 |
| url | https://arxiv.org/abs/2410.18865 |