Tensor Product of Degenerate Principal Series and Local Theta Correspondence
نویسندگان
چکیده
منابع مشابه
Degenerate Principal Series and Local Theta Correspondence
In this paper we determine the structure of the natural Ũ(n, n) module Ωp,q(l) which is the Howe quotient corresponding to the determinant character det of U(p, q). We first give a description of the tempered distributions on Mp+q,n(C) which transform according to the character det−l under the linear action of U(p, q). We then show that after tensoring with a character, Ωp,q(l) can be embedded ...
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Let (G, G) be one of the following complex dual pairs: (O(m,C), Sp(2n,C)), (GL(m,C),GL(2n,C)), (Sp(2m,C),O(4n,C)). We determine the relationship between the space ofG-coinvariants and certain degenerate principal series representations of G. We also show that the space of G-invariant distributions is generated by the Dirac distribution as a G-representation. Introduction and main results Let G ...
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The main purpose of this article is to supplement the authors’ results on degenerate principal series representations of real symplectic groups with the analogous results for metaplectic groups. The basic theme, as in the previous case, is that their structures are anticipated by certain natural subrepresentations constructed from Howe correspondence. This supplement is necessary as these repre...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2001
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3786