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arXiv · 1703.09475

Some results on reducibility of parabolic induction for classical groups

Erez Lapid·Marko Tadić
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Abstract

Given a (complex, smooth) irreducible representation $π$ of the general linear group over a non-archimedean local field and an irreducible supercuspidal representation $σ$ of a classical group, we show that the (normalized) parabolic induction $π\rtimesσ$ is reducible if there exists $ρ$ in the supercuspidal support of $π$ such that $ρ\rtimesσ$ is reducible. In special cases we also give irreducibility criteria for $π\rtimesσ$ when the above condition is not satisfied.

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Erez Lapid, Marko Tadić. 2017-03-28. Some results on reducibility of parabolic induction for classical groups. https://doi.org/10.1353/ajm.2020.0014

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