Howe duality over finite fields III: Full computation and the Gurevich-Howe conjectures
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910121493266432 |
|---|---|
| author | Kriz, Sophie |
| author_facet | Kriz, Sophie |
| contents | In this third paper in a series on type I Howe duality for finite fields, we give a complete description of the restriction of the oscillator representation over a finite field to products of dual pairs of symplectic and orthogonal groups in all cases that occur. We also provide a dictionary with the notation of S.-Y. Pan, who identified which tensor products of irreducible representations occur with non-zero multiplicity. As an application, we give a recursive construction of all irreducible complex representations of finite symplectic and orthogonal groups and a recursive formula for the characters of unipotent cuspidal representations. We also give a proof of the Gurevich-Howe rank and exhaustion conjectures for type C groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22986 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Howe duality over finite fields III: Full computation and the Gurevich-Howe conjectures Kriz, Sophie Representation Theory 11F27, 20C33, 20G40 In this third paper in a series on type I Howe duality for finite fields, we give a complete description of the restriction of the oscillator representation over a finite field to products of dual pairs of symplectic and orthogonal groups in all cases that occur. We also provide a dictionary with the notation of S.-Y. Pan, who identified which tensor products of irreducible representations occur with non-zero multiplicity. As an application, we give a recursive construction of all irreducible complex representations of finite symplectic and orthogonal groups and a recursive formula for the characters of unipotent cuspidal representations. We also give a proof of the Gurevich-Howe rank and exhaustion conjectures for type C groups. |
| title | Howe duality over finite fields III: Full computation and the Gurevich-Howe conjectures |
| topic | Representation Theory 11F27, 20C33, 20G40 |
| url | https://arxiv.org/abs/2506.22986 |