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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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On the theta correspondence for $(\mathrm {GSp}(4), \mathrm {GSO}(4,2))$ and Shalika periods
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by Kazuki Morimoto PDF
Represent. Theory 18 (2014), 28-87 Request permission


We consider both local and global theta correspondences for $\mathrm {GSp}_4$ and $\mathrm {GSO}_{4,2}$. Because of the accidental isomorphism $\mathrm {PGSO}_{4,2} \simeq \mathrm {PGU}_{2,2}$, these correspondences give rise to those between $\mathrm {GSp}_4$ and $\mathrm {GU}_{2,2}$ for representations with trivial central characters. In the global case, using this relation, we characterize representations with trivial central character, which have Shalika period on $\mathrm {GU}(2,2)$ by theta correspondences. Moreover, in the local case, we consider a similar relationship for irreducible admissible representations without an assumption on the central character.
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Additional Information
  • Kazuki Morimoto
  • Affiliation: Department of Mathematics, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
  • Address at time of publication: Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
  • Email:
  • Received by editor(s): March 11, 2013
  • Received by editor(s) in revised form: November 1, 2013
  • Published electronically: April 16, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Represent. Theory 18 (2014), 28-87
  • MSC (2010): Primary 11F27; Secondary 22E50
  • DOI:
  • MathSciNet review: 3193382