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

Authors:	Chen-bo Zhu

Affiliation:	Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260

Abstract:	Let be the reductive dual pair . We show that if is a representation of (respectively ) obtained from duality correspondence with some representation of (respectively ), then its Gelfand-Kirillov dimension is less than or equal to $(p+q)(2n-frac{p+q-1}{2})$ (respectively $2n(p+q-frac{2n+1}{2})$ ).

Keywords:	Classical groups duality correspondence Gelfand-Kirillov dimension

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