Heredity of Whittaker models on the metaplectic group

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Heredity of Whittaker Models on the Metaplectic Group

and the Whittaker models of the inducing representation π M (cf. Theorem 2 of [4]). In this paper, Rodier’s theorem on the “heredity” of Whittaker models is extended to the non-algebraic setting of the n-fold metaplectic cover G̃ of G, where n is a positive integer such that F contains all of the n-th roots of unity. The main result is stated as a theorem in §2. In order to illustrate the situat...

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Whittaker Coefficients of Metaplectic Eisenstein Series

We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However they are not Eulerian and the standard methods to compute them in the reductive case do not apply to covers. For “cominuscule” maximal parabolics, we give an e...

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A Corollary to Bernstein’s Theorem and Whittaker Functionals on the Metaplectic Group

In this paper, we extend and apply a remarkable theorem due to Bernstein, which was proved in a letter to Piatetski-Shapiro in the fall of 1985 [3]. The theorem is quite useful for establishing analytic continuation and rationality results in a variety of settings in the study of automorphic forms and L-functions, such as in the theory of local intertwining operators and local coefficients for ...

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ژورنال

عنوان ژورنال: Pacific Journal of Mathematics

سال: 1998

ISSN: 0030-8730

DOI: 10.2140/pjm.1998.185.89