Some Results on Reducibility of Parabolic Induction for Classical Groups

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Date
2017-03-30MFO Scientific Program
Research in Pairs 2016Series
Oberwolfach Preprints;2017,09Author
Lapid, Erez
Tadić, Marko
Metadata
Show full item recordOWP-2017-09
Abstract
Given a (complex, smooth) irreducible representation $\pi$ of the general
linear group over a non-archimedean local field and an irreducible
supercuspidal representation $\sigma$ of a classical group, we show that the
(normalized) parabolic induction $\pi\rtimes\sigma$ is reducible if there
exists $\rho$ in the supercuspidal support of $\pi$ such that
$\rho\rtimes\sigma$ is reducible. In special cases we also give irreducibility
criteria for $\pi\rtimes\sigma$ when the above condition is not satisfied.