On disjointness of linear models and degenerate Whittaker models
| Autor: | Eitan Sayag, Mahendra Kumar Verma |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Distribution (number theory) 010102 general mathematics Degenerate energy levels Linear model Field (mathematics) 010103 numerical & computational mathematics Rank (differential topology) 01 natural sciences Section (category theory) Finite field 0101 mathematics Local field Mathematics |
| Zdroj: | Journal of Number Theory. 207:56-82 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2019.04.003 |
| Popis: | In this article we reprove and generalize a result of N. Matringe [12] concerning generic representations of GL n ( F ) that admits a linear model with respect to a maximal Levi subgroup GL p ( F ) × GL q ( F ) , where F is a non-archimedean field. He showed that in this case | p − q | ≤ 1 . We extend this result to the case where F is a finite field or a local field of characteristic different from 2. Further, we study non-generic representations of GL n ( F ) and describe their possible linear models in terms of their rank r ( π ) (see Section 6 ). Our arguments are based on the method of Gelfand-Kazhdan and the theory of distribution and provide uniform proofs for finite, p-adic and archimedean fields. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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