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Proceedings of the American Mathematical Society

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A result on the Gelfand-Kirillov dimension
of representations of classical groups


Author: Chen-bo Zhu
Journal: Proc. Amer. Math. Soc. 126 (1998), 3125-3130
MSC (1991): Primary 22E46, 22E47
DOI: https://doi.org/10.1090/S0002-9939-98-04418-9
MathSciNet review: 1452837
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Abstract: Let $(G,G')$ be the reductive dual pair $(O(p,q),Sp(2n,\mathbb{R}))$. We show that if $\pi $ is a representation of $Sp(2n,\mathbb{R})$ (respectively $O(p,q)$) obtained from duality correspondence with some representation of $O(p,q)$ (respectively $Sp(2n,\mathbb{R})$), then its Gelfand-Kirillov dimension is less than or equal to
$(p+q)(2n-\frac{p+q-1}{2})$ (respectively $2n(p+q-\frac{2n+1}{2})$).


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Additional Information

Chen-bo Zhu
Affiliation: Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260
Email: matzhucb@leonis.nus.sg.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04418-9
Keywords: Classical groups, duality correspondence, Gelfand-Kirillov dimension
Received by editor(s): November 4, 1996
Received by editor(s) in revised form: February 27, 1997
Communicated by: Roe Goodman
Article copyright: © Copyright 1998 American Mathematical Society