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Representation Theory
Representation Theory
ISSN 1088-4165

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


Author: Steve Rallis
Journal: Represent. Theory 17 (2013), 176-179
MSC (2010): Primary 22E55
Posted: March 4, 2013
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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.


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Additional Information

Steve Rallis
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210

DOI: http://dx.doi.org/10.1090/S1088-4165-2013-00428-4
PII: S 1088-4165(2013)00428-4
Received by editor(s): November 8, 2011
Received by editor(s) in revised form: August 20, 2012, and October 2, 2012
Posted: 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.