On local character expansions for principal series representations of general linear groups
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909211222343680 |
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| author | Gurevich, Maxim |
| author_facet | Gurevich, Maxim |
| contents | We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical case, expresses the expansion in terms of dimensions of degenerate Whittaker models. The second gives a closed expression in terms of values of Kazhdan-Lusztig polynomials of a suitable permutation group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On local character expansions for principal series representations of general linear groups Gurevich, Maxim Representation Theory We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical case, expresses the expansion in terms of dimensions of degenerate Whittaker models. The second gives a closed expression in terms of values of Kazhdan-Lusztig polynomials of a suitable permutation group. |
| title | On local character expansions for principal series representations of general linear groups |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2405.16872 |