On the degenerate principal series of complex symplectic groups
نویسندگان
چکیده
منابع مشابه
Degenerate Principal Series and Local Theta Correspondence Iii: the Case of Complex Groups
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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Let S̃p(n,R) be the universal covering of the symplectic group. In this paper, we study the restrictions of the degenerate unitary principal series I( , t) of S̃p(n,R) onto S̃p(p,R)S̃p(n − p,R). We prove that if n ≥ 2p , I( , t)| S̃p(p,R)S̃p(n−p,R) is unitarily equivalent to an L 2 -space of sections of a homogeneous line bundle L(S̃p(n − p,R) × G̃L(n−2p)N C ,t+ρ) (see Theorem 1.1). We further study th...
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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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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2012.02.013