ON -DISTINGUISHED REPRESENTATIONS OF THE QUASI-SPLIT UNITARY GROUPS
| Autor: | Omer Offen, Arnab Mitra |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Conjecture General Mathematics 010102 general mathematics Extension (predicate logic) 01 natural sciences Unitary state Base change Transfer (group theory) Quadratic equation Unitary group 0103 physical sciences Tempered representation 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Journal of the Institute of Mathematics of Jussieu. 20:225-276 |
| ISSN: | 1475-3030 1474-7480 |
| DOI: | 10.1017/s1474748019000161 |
| Popis: | We study$\text{Sp}_{2n}(F)$-distinction for representations of the quasi-split unitary group$U_{2n}(E/F)$in$2n$variables with respect to a quadratic extension$E/F$of$p$-adic fields. A conjecture of Dijols and Prasad predicts that no tempered representation is distinguished. We verify this for a large family of representations in terms of the Mœglin–Tadić classification of the discrete series. We further study distinction for some families of non-tempered representations. In particular, we exhibit$L$-packets with no distinguished members that transfer under base change to$\text{Sp}_{2n}(E)$-distinguished representations of$\text{GL}_{2n}(E)$. |
| Databáze: | OpenAIRE |
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