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Representation Theory

ISSN 1088-4165

 
 

 

Complement to the appendix of: “On the Howe duality conjecture”


Author: \fbox{Steve Rallis}
Journal: Represent. Theory 17 (2013), 176-179
MSC (2010): Primary 22E55
DOI: https://doi.org/10.1090/S1088-4165-2013-00428-4
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.


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Additional Information

\fbox{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.