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

Hiraku Atobe

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

Representation Theory 2022-04-26 v2

Authors: Hiraku Atobe

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.

Keywords

p-adic classical groups parabolically induced representations socles Speh representations Arthur type representations complementary series

Cite

@article{arxiv.2109.12819,
  title  = {On the socles of certain parabolically induced representations of $p$-adic classical groups},
  author = {Hiraku Atobe},
  journal= {arXiv preprint arXiv:2109.12819},
  year   = {2022}
}

Comments

Final version. arXiv admin note: text overlap with arXiv:2012.07232

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

Abstract

Keywords

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