Journal of the Mathematical Society of Japan

Generalized Whittaker functions on GSp(2,R) associated with indefinite quadratic forms

Tomonori MORIYAMA

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Abstract

We study the generalized Whittaker models for G = GSp(2,R) associated with indefinite binary quadratic forms when they arise from two standard representations of G: (i) a generalized principal series representation induced from the non-Siegel maximal parabolic subgroup and (ii) a (limit of) large discrete series representation. We prove the uniqueness of such models with moderate growth property. Moreover we express the values of the corresponding generalized Whittaker functions on a one-parameter subgroup of G in terms of the Meijer G-functions.

Article information

Source
J. Math. Soc. Japan, Volume 63, Number 4 (2011), 1203-1262.

Dates
First available in Project Euclid: 27 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1319721140

Digital Object Identifier
doi:10.2969/jmsj/06341203

Mathematical Reviews number (MathSciNet)
MR2855812

Zentralblatt MATH identifier
1268.22018

Subjects
Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]

Keywords
generalized Whittaker functions Fourier expansions of automorphic forms on GSp(2) the Meijer G-functions

Citation

MORIYAMA, Tomonori. Generalized Whittaker functions on GSp (2, R ) associated with indefinite quadratic forms. J. Math. Soc. Japan 63 (2011), no. 4, 1203--1262. doi:10.2969/jmsj/06341203. https://projecteuclid.org/euclid.jmsj/1319721140


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References

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