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Relative Discrete Series Representations for Two Quotients of p-adic GLn
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 6 / 01 December 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1339-1372
- Print publication:
- 01 December 2018
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- Article
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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.
