Standard modules of affine Hecke algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908979514310656 |
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| author | Dawydiak, Stefan |
| author_facet | Dawydiak, Stefan |
| contents | Let $G$ be a connected reductive group defined and split over a non-archimedean local field $F$. We give a new geometric proof of a special case of a recent theorem of Solleveld. Namely, we show that the class of standard Iwahori-spherical $G(F)$-representations, a notion a priori dependent on the coefficient field being the complex numbers, is actually defined over $\overline{\mathbb{Q}_\ell}$.
An unpublished theorem of Clozel, proven with global techniques, says that the class of essentially square-integrable representations is also defined over $\overline{\mathbb{Q}_\ell}$. As an application of our main result, we give a local proof of this theorem for inner forms of $\mathrm{GL}_n$, as well as showing that standard representations of these groups are defined over $\overline{\mathbb{Q}_\ell}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14953 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Standard modules of affine Hecke algebras Dawydiak, Stefan Representation Theory 20C08 (primary), 22E50 (secondary), 14C15 (secondary) Let $G$ be a connected reductive group defined and split over a non-archimedean local field $F$. We give a new geometric proof of a special case of a recent theorem of Solleveld. Namely, we show that the class of standard Iwahori-spherical $G(F)$-representations, a notion a priori dependent on the coefficient field being the complex numbers, is actually defined over $\overline{\mathbb{Q}_\ell}$. An unpublished theorem of Clozel, proven with global techniques, says that the class of essentially square-integrable representations is also defined over $\overline{\mathbb{Q}_\ell}$. As an application of our main result, we give a local proof of this theorem for inner forms of $\mathrm{GL}_n$, as well as showing that standard representations of these groups are defined over $\overline{\mathbb{Q}_\ell}$. |
| title | Standard modules of affine Hecke algebras |
| topic | Representation Theory 20C08 (primary), 22E50 (secondary), 14C15 (secondary) |
| url | https://arxiv.org/abs/2602.14953 |