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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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Complement to the appendix of: “On the Howe duality conjecture”
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by Steve Rallis PDF
Represent. Theory 17 (2013), 176-179 Request permission


Let ${\mathbb F}$ be a local field, nonarchimedean and of characteristic not 2. Let $(V,Q)$ be a nondegenerate quadratic space over ${\mathbb F}$, of dimension $n$. Let $M_r$ be the direct sum of $r$ copies of $V$. We prove that, for $r<n$ there is no nonzero distribution on $M_r$ which under the action of the orthogonal group transforms according to the character determinant.
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Additional Information
  • Steve Rallis
  • Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
  • Received by editor(s): November 8, 2011
  • Received by editor(s) in revised form: August 20, 2012, and October 2, 2012
  • Published electronically: March 4, 2013
  • Additional Notes: Sadly, the author passed away on April 17, 2012
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 17 (2013), 176-179
  • MSC (2010): Primary 22E55
  • DOI:
  • MathSciNet review: 3028189