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Representations induced from the Zelevinsky segment and discrete series in the half-integral case

  • Ivan Matić ORCID logo EMAIL logo
Published/Copyright: November 7, 2020

Abstract

Let Gn denote either the group SO(2n+1,F) or Sp(2n,F) over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form Δσ, where Δ denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of Gn. We determine the composition series of Δσ in the case when Δ=[νaρ,νbρ] where a is half-integral.

MSC 2010: 22E35; 22E50; 11F70

Communicated by Freydoon Shahidi


Award Identifier / Grant number: IP-2018-01-3628

Funding statement: This work has been supported in part by Croatian Science Foundation under the project IP-2018-01-3628.

Acknowledgements

The author would like to thank Goran Muić for his suggestion to study this subject. The author would like to thank the referee for his or her careful reading, useful comments and suggestions.

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Received: 2020-02-29
Revised: 2020-10-11
Published Online: 2020-11-07
Published in Print: 2021-01-01

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