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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the singular rank of a representation


Author: Jian-Shu Li
Journal: Proc. Amer. Math. Soc. 106 (1989), 567-571
MSC: Primary 22E46; Secondary 22E45, 22E47
MathSciNet review: 961413
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Abstract: Consider the reductive dual pair $ ({\text{S}}{{\text{p}}_{2n}},{{\text{O}}_{p,q}})$. We prove that if $ \pi $ is a representation of $ {\text{S}}{{\text{p}}_{2n}}$ coming from duality correspondence with some representation of $ {{\text{O}}_{p,q}}$ then the wave front set of $ \pi $ has rank $ \leq p + q$. For $ p + q < n$ this implies a result stated (but not proved) by Howe.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0961413-8
PII: S 0002-9939(1989)0961413-8
Keywords: Wave front sets, reductive dual pairs
Article copyright: © Copyright 1989 American Mathematical Society