A reformulation of the conjecture of Prasad and Takloo-Bighash
Uložené v:
| Názov: | A reformulation of the conjecture of Prasad and Takloo-Bighash |
|---|---|
| Autori: | Miyu Suzuki |
| Zdroj: | Journal of Algebra. 680:174-204 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Elsevier BV, 2025. |
| Rok vydania: | 2025 |
| Predmety: | Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), Mathematics - Representation Theory |
| Popis: | Prasad and Takloo-Bighash proposed a conjecture which predicts a necessary condition in terms of epsilon factors for representations of $\mathrm{GL}_n(F)$ and its inner forms to have linear periods. In this rather expository article, we reformulate their conjecture in the following form: The distinguished members in each generic $L$-packet $Π_ϕ$ are determined by the characters of the component group $S_ϕ$ and local epsilon factors. We follow Aubert et al.\,for the definitions of the $L$-packets and the component groups. We observe that under some hypotheses, the reformulated conjecture follows from the conjectural multiplicity formula recently proposed by Chen Wan for general spherical varieties and the conjectural integral formula for epsilon factors which we propose in this article. Dedicated to Tamotsu Ikeda on the occasion of his sixtieth birthday |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2025.05.007 |
| DOI: | 10.48550/arxiv.2312.16393 |
| Prístupová URL adresa: | http://arxiv.org/abs/2312.16393 |
| Rights: | Elsevier TDM arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....d4ce9ab0353ac769ddb36bb770a56c61 |
| Databáza: | OpenAIRE |
Full Text Finder 
Nájsť tento článok vo Web of Science | Abstrakt: | Prasad and Takloo-Bighash proposed a conjecture which predicts a necessary condition in terms of epsilon factors for representations of $\mathrm{GL}_n(F)$ and its inner forms to have linear periods. In this rather expository article, we reformulate their conjecture in the following form: The distinguished members in each generic $L$-packet $Π_ϕ$ are determined by the characters of the component group $S_ϕ$ and local epsilon factors. We follow Aubert et al.\,for the definitions of the $L$-packets and the component groups. We observe that under some hypotheses, the reformulated conjecture follows from the conjectural multiplicity formula recently proposed by Chen Wan for general spherical varieties and the conjectural integral formula for epsilon factors which we propose in this article.<br />Dedicated to Tamotsu Ikeda on the occasion of his sixtieth birthday |
|---|---|
| ISSN: | 00218693 |
| DOI: | 10.1016/j.jalgebra.2025.05.007 |