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Representation Theory

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Complement to the appendix of: ``On the Howe duality conjecture''

Author: Steve Rallis
Journal: Represent. Theory 17 (2013), 176-179
MSC (2010): Primary 22E55
Published electronically: March 4, 2013
MathSciNet review: 3028189
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Abstract: 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.

References [Enhancements On Off] (What's this?)

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  • [R] S. Rallis, On the Howe duality conjecture, Compositio Math. 51 (1984), no. 3, 333-399. MR 743016 (85g:22034)

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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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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