منابع مشابه
Whittaker Functions on Metaplectic Groups
The theory of Whittaker functions is of crucial importance in the classical study of automorphic forms on adele groups. Motivated by the appearance of Whittaker functions for covers of reductive groups in the theory of multiple Dirichlet series, we provide a study of Whittaker functions on metaplectic covers of reductive groups over local fields. Thesis Supervisor: Benjamin Brubaker Title: Assi...
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In 1952, Gelfand and Fomin noticed that classical modular forms were related to representations of SL2(R). As a result of this realization, Gelfand later defined GLr automorphic forms via representation theory. A metaplectic form is just an automorphic form defined on a cover of GLr, called a metaplectic group. In this talk, we will carefully construct the metaplectic covers of GL2(F) where F i...
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M. Hanzer and I. Matić have proved that the genuine unitary principal series representations of the metaplectic groups are irreducible. A simple consequence of that paper is a criterion for the irreducibility of the non-unitary principal series representations of the metaplectic groups that we give in this paper.
متن کاملPrincipal Series Representations of Metaplectic Groups
We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order n. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.
متن کاملLocal Coefficient Matrices of Metaplectic Groups
The principal series representations of the n-fold metaplectic covers of the general linear group GLr(F) were described in the foundational paper “Metaplectic Forms,” by Kazhdan and Patterson (1984). In this paper, we study the local coefficient matrices for a certain class of principal series representations over GL2(F), where F is a nonarchimedean local field. The local coefficient matrices c...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2020
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12318