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

Zhu, Chen-bo

doi:10.1090/S0002-9939-98-04418-9

A result on the Gelfand-Kirillov dimension of representations of classical groups
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Proc. Amer. Math. Soc. 126 (1998), 3125-3130 Request permission

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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