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

2021/09/27 by Atobe, Hiraku · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2109.12819

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 are called complementary series.

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• Unitary dual of p-adic split SO_2n+1 and Sp_2n: The good parity case (and slightly beyond)

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