Twisted Jacquet modules: a conjecture of D. Prasad
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909340780199936 |
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| author | Nadimpalli, Santosh Sheth, Mihir |
| author_facet | Nadimpalli, Santosh Sheth, Mihir |
| contents | In this note, we study the twisted Jacquet modules of sub-quotients of principal series representations of ${\rm GL}_2(D)$ where $D$ is a division algebra over a non-archimedean local field $F$. We begin with a proof of a conjecture due to D. Prasad on twisted Jacquet modules of Speh representations of ${\rm GL}_2(D)$ when $D$ is the quaternionic division algebra. Later, when $D$ is an arbitrary division algebra over $F$, we focus on depth-zero principal series and compute the dimensions of twisted Jacquet modules of generalised Speh representations and investigate their structure explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00735 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twisted Jacquet modules: a conjecture of D. Prasad Nadimpalli, Santosh Sheth, Mihir Representation Theory Number Theory 11F85 (Primary), 22E50 (Secondary) In this note, we study the twisted Jacquet modules of sub-quotients of principal series representations of ${\rm GL}_2(D)$ where $D$ is a division algebra over a non-archimedean local field $F$. We begin with a proof of a conjecture due to D. Prasad on twisted Jacquet modules of Speh representations of ${\rm GL}_2(D)$ when $D$ is the quaternionic division algebra. Later, when $D$ is an arbitrary division algebra over $F$, we focus on depth-zero principal series and compute the dimensions of twisted Jacquet modules of generalised Speh representations and investigate their structure explicitly. |
| title | Twisted Jacquet modules: a conjecture of D. Prasad |
| topic | Representation Theory Number Theory 11F85 (Primary), 22E50 (Secondary) |
| url | https://arxiv.org/abs/2310.00735 |