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ON THE DISTINCTION OF IWAHORI-SPHERICAL DISCRETE SERIES REPRESENTATIONS
Published online by Cambridge University Press: 17 April 2024
Abstract
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.
Keywords
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- Research Article
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- Copyright
- © The Author(s), 2024. Published by Cambridge University Press
References
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