On reducibility of induced representations of odd unitary groups: the depth zero case
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917730221817856 |
|---|---|
| author | Repaka, Subha Sandeep |
| author_facet | Repaka, Subha Sandeep |
| contents | We study a problem concerning parabolic induction in certain $p$-adic unitary groups. More precisely, for $E/F$ a quadratic extension of $p$-adic fields the associated unitary group $G=\mathrm{U}(n,n+1)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E) \times \mathrm{U}_1(E)$. Let $π$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $ι_P^G π$ is reducible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_00413 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On reducibility of induced representations of odd unitary groups: the depth zero case Repaka, Subha Sandeep Representation Theory Primary 22E50, Secondary 11F70 We study a problem concerning parabolic induction in certain $p$-adic unitary groups. More precisely, for $E/F$ a quadratic extension of $p$-adic fields the associated unitary group $G=\mathrm{U}(n,n+1)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E) \times \mathrm{U}_1(E)$. Let $π$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $ι_P^G π$ is reducible. |
| title | On reducibility of induced representations of odd unitary groups: the depth zero case |
| topic | Representation Theory Primary 22E50, Secondary 11F70 |
| url | https://arxiv.org/abs/2101.00413 |