Symplectic period for a representation of $GL_n(D)$
| Autor: | Sharma, Hariom, Verma, Mahendra Kumar |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $D$ be a quaternion division algebra over a non-archimedean local field $K$ of characteristic zero, and let $Sp_n(D)$ be the unique non-split inner form of the symplectic group $Sp_{2n}(K)$. This paper classifies the irreducible admissible representations of $GL_{n}(D)$ with a symplectic period for $n = 3$ and $4$, i.e., those irreducible admissible representations $(\pi, V)$ of $GL_{n}(D)$ which have a linear functional $l$ on $V$ such that $l(\pi(h)v) = l(v)$ for all $v \in V$ and $h \in Sp_n(D)$. Our results also contain all unitary representations having a symplectic period, as stated in Prasad's conjecture. Comment: 26 pages, comments are welcome |
| Databáze: | arXiv |
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