Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.15772 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929430705733632 |
|---|---|
| author | Cohen, Jonathan |
| author_facet | Cohen, Jonathan |
| contents | Let $F$ be a $p$-adic field and $(π, V)$ an irreducible complex representation of $G=GSp(4, F)$ with trivial central character. Let ${\rm Si}(\mathfrak{p}^2)\subset G$ denote the Siegel congruence subgroup of level $\mathfrak{p}^2$ and $u\in N_G({\rm Si}(\mathfrak{p}^2))$ the Atkin-Lehner element. We compute the dimension of the space of ${\rm Si}(\mathfrak{p}^2)$-fixed vectors in $V$ as well as the signatures of the involutions $π(u)$ acting on these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Siegel $\mathfrak{p}^2$ Vectors for Representations of $GSp(4)$ Cohen, Jonathan Representation Theory Number Theory 11F70 Let $F$ be a $p$-adic field and $(π, V)$ an irreducible complex representation of $G=GSp(4, F)$ with trivial central character. Let ${\rm Si}(\mathfrak{p}^2)\subset G$ denote the Siegel congruence subgroup of level $\mathfrak{p}^2$ and $u\in N_G({\rm Si}(\mathfrak{p}^2))$ the Atkin-Lehner element. We compute the dimension of the space of ${\rm Si}(\mathfrak{p}^2)$-fixed vectors in $V$ as well as the signatures of the involutions $π(u)$ acting on these spaces. |
| title | Siegel $\mathfrak{p}^2$ Vectors for Representations of $GSp(4)$ |
| topic | Representation Theory Number Theory 11F70 |
| url | https://arxiv.org/abs/2407.15772 |