Relative Discrete Series Representations for Two Quotients of p-adic GLn

Smith, Jerrod Manford

Canadian journal of mathematics, Tome 70 (2018) no. 6, pp. 1339-1372

Résumé

We provide an explicit construction of representations in the discrete spectrum of two $p$ -adic symmetric spaces. We consider $\text{G}{{\text{L}}_{n}}\left( F \right)\,\times \,\text{G}{{\text{L}}_{n}}\left( F \right)\backslash \text{G}{{\text{L}}_{2n}}\left( F \right)$ and $\text{G}{{\text{L}}_{n}}\left( F \right)\,\backslash \text{G}{{\text{L}}_{n}}\left( E \right)$ , where $E$ is a quadratic Galois extension of a nonarchimedean local field $F$ of characteristic zero and odd residual characteristic. The proof of the main result involves an application of a symmetric space version of Casselman’s Criterion for square integrability due to Kato and Takano.

Détail

DOI : 10.4153/CJM-2017-047-7

Mots-clés : 22E50, 22E35, p-adic symmetric space, relative discrete series, Casselman’s Criterion