Generic representations of metaplectic groups and their theta lifts
نویسندگان
چکیده
منابع مشابه
Principal 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.
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Let X be an even dimensional symmetric bilinear space defined over a totally real number field F with adeles A, and let σ = ⊗vσv be an irreducible tempered cuspidal automorphic representation of O(X,A). We give a sufficient condition for the nonvanishing of the theta lift Θn(σ) of σ to the symplectic group Sp(n,A) (2n by 2n matrices) for 2n ≥ dimX for a large class of X. As a corollary, we show...
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We define a regularized theta lift for orthogonal groups over totally real fields generalizing work of Borcherds. The lift takes harmonic ‘Whittaker forms’ to automorphic Green functions and weakly holomorphic Whittaker forms to meromorphic modular forms on orthogonal groups with zeros and poles supported on special divisors.
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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.
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Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension G̃ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for G̃ and its applications to the study of Hecke algebras via a Satake is...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2020
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-020-02563-z