Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 1452837
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $2n(p+q-\frac{2n+1}{2})$).

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 22E46, 22E47

Retrieve articles in all journals with MSC (1991): 22E46, 22E47

Additional Information

Chen-bo Zhu
Affiliation: Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260

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