Guardat en:
| Autors principals: | , |
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| Format: | Preprint |
| Publicat: |
2025
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2506.04449 |
| Etiquetes: |
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Taula de continguts:
- Under a largeness assumption on the size of the residue field, we give an explicit description of the positive-depth Deligne--Lusztig induction of unramified elliptic pairs $(T,θ)$. When $θ$ is regular, we show that positive-depth Deligne--Lusztig induction gives a geometric realization of Kaletha's Howe-unramified regular $L$-packets. This is obtained as an immediate corollary of a very simple "litmus test" characterization theorem which we foresee will have interesting future applications to small-$p$ constructions. We next define and analyze Green functions of two different origins: Yu's construction (algebra) and positive-depth Deligne--Lusztig induction (geometry). Using this, we deduce a comparison result for arbitrary $θ$ from the regular setting. As a further application of our comparison isomorphism, we prove the positive-depth Springer hypothesis in the $0$-toral setting and use it to give a geometric explanation for the appearance of orbital integrals in supercuspidal character formulae.