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Title: Degenerate principal series and local theta correspondence soo
Authors: Lee, T. 
Zhu, C.-B. 
Keywords: Degenerate principal series
Gelfand-kirillov dimension
Howe quotients
Local theta correspondence
Unitary representations
Issue Date: 1998
Citation: Lee, T.,Zhu, C.-B. (1998). Degenerate principal series and local theta correspondence soo. Transactions of the American Mathematical Society 350 (12) : 5017-5046. ScholarBank@NUS Repository.
Abstract: ABSTRACT. 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 detl 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 into one of the degenerate series representations of U(n, n). This allows us to determine the module structure of Ωp,q(l). Moreover we show that certain irreducible constituents in the degenerate series can be identified with some of these representations Ωp,q(l) or their irreducible quotients. We also compute the Gelfand-Kirillov dimensions of the irreducible constituents of the degenerate series. © 1998 American Mathematical Society.
Source Title: Transactions of the American Mathematical Society
ISSN: 00029947
Appears in Collections:Staff Publications

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