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ON THE DISTINCTION OF IWAHORI-SPHERICAL DISCRETE SERIES REPRESENTATIONS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 24 / Issue 1 / January 2025
- Published online by Cambridge University Press:
- 17 April 2024, pp. 1-15
- Print publication:
- January 2025
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- Article
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Let
$E/F$ be a quadratic unramified extension of non-archimedean local fields and 
$\mathbb H$ a simply connected semisimple algebraic group defined and split over F. We establish general results (multiplicities, test vectors) on 
${\mathbb H} (F)$-distinguished Iwahori-spherical representations of 
${\mathbb H} (E)$. For discrete series Iwahori-spherical representations of 
${\mathbb H} (E)$, we prove a numerical criterion of 
${\mathbb H} (F)$-distinction. As an application, we classify the 
${\mathbb H} (F)$-distinguished discrete series representations of 
${\mathbb H} (E)$ corresponding to degree 
$1$ characters of the Iwahori-Hecke algebra.
