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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Nonvanishing of a certain sesquilinear form in the theta correspondence
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by Hongyu He
Represent. Theory 5 (2001), 437-454
Published electronically: October 30, 2001


Suppose $2n+1 \geq p+q$. In an earlier paper in 2000 we study a certain sesquilinear form $(,)_{\pi }$ introduced by Jian-Shu Li in 1989. For $\pi$ in the semistable range of $\theta (MO(p,q) \rightarrow MSp_{2n}(\mathbb {R}))$, if $(,)_{\pi }$ does not vanish, then it induces a sesquilinear form on $\theta (\pi )$. In another work in 2000 we proved that $(,)_{\pi }$ is positive semidefinite under a mild growth condition on the matrix coefficients of $\pi$. In this paper, we show that either $(,)_{\pi }$ or $(,)_{\pi \otimes \det }$ is nonvanishing. These results combined with one result of Przebinda suggest the existence of certain unipotent representations of $Mp_{2n}(\mathbb {R})$ beyond unitary representations of low rank.
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Bibliographic Information
  • Hongyu He
  • Affiliation: Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303-3083
  • Email:
  • Received by editor(s): April 24, 2001
  • Received by editor(s) in revised form: July 30, 2001
  • Published electronically: October 30, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 437-454
  • MSC (2000): Primary 22E45
  • DOI:
  • MathSciNet review: 1870597