On the socles of certain parabolically induced representations of 𝑝-adic classical groups

Atobe, Hiraku

doi:10.1090/ert/612

On the socles of certain parabolically induced representations of $p$-adic classical groups
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by Hiraku Atobe

Represent. Theory 26 (2022), 515-541

DOI: https://doi.org/10.1090/ert/612

Published electronically: April 25, 2022

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Abstract:

In this paper, we consider representations of $p$-adic classical groups parabolically induced from the products of shifted Speh representations and unitary representations of Arthur type of good parity. We describe how to compute the socles (the maximal semisimple subrepresentations) of these representations. As a consequence, we can determine whether these representations are reducible or not. In particular, our results produce many unitary representations, which appear in the complementary series.

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