The scalar product formula for parahoric Deligne--Lusztig induction
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915507093897216 |
|---|---|
| author | Chan, Charlotte |
| author_facet | Chan, Charlotte |
| contents | Parahoric Deligne--Lusztig induction gives rise to positive-depth representations of parahoric subgroups of $p$-adic groups. The most fundamental basic question about parahoric Deligne--Lusztig induction is whether it satisfies the scalar product formula. We resolve this conjecture for all Howe-factorizable split-generic pairs $(T,θ)$ -- in particular, for all characters $θ$ when $T$ is elliptic and $p$ is not a torsion prime for the root system of the $p$-adic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The scalar product formula for parahoric Deligne--Lusztig induction Chan, Charlotte Representation Theory Algebraic Geometry Parahoric Deligne--Lusztig induction gives rise to positive-depth representations of parahoric subgroups of $p$-adic groups. The most fundamental basic question about parahoric Deligne--Lusztig induction is whether it satisfies the scalar product formula. We resolve this conjecture for all Howe-factorizable split-generic pairs $(T,θ)$ -- in particular, for all characters $θ$ when $T$ is elliptic and $p$ is not a torsion prime for the root system of the $p$-adic group. |
| title | The scalar product formula for parahoric Deligne--Lusztig induction |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2405.00671 |