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December 2020 Special functions associated with K -types of degenerate principal series of Sp ( n , C )
Grégory Mendousse
Kyoto J. Math. 60(4): 1373-1398 (December 2020). DOI: 10.1215/21562261-2019-0065

Abstract

We study K -types of degenerate principal series of Sp ( n , C ) by using two realizations of these infinite-dimensional representations. The first model we use is the classical compact picture; the second model is conjugate to the noncompact picture via an appropriate partial Fourier transform. In the first case, we find a family of K -finite vectors that can be expressed as solutions of specific hypergeometric differential equations; the second case leads to a family of K -finite vectors whose expressions involve Bessel functions.

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Grégory Mendousse. "Special functions associated with K -types of degenerate principal series of Sp ( n , C ) ." Kyoto J. Math. 60 (4) 1373 - 1398, December 2020. https://doi.org/10.1215/21562261-2019-0065

Information

Received: 21 June 2018; Revised: 4 November 2018; Accepted: 6 December 2018; Published: December 2020
First available in Project Euclid: 6 October 2020

MathSciNet: MR4175812
Digital Object Identifier: 10.1215/21562261-2019-0065

Subjects:
Primary: 22E46
Secondary: 33C10, 33C55, 43A75

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 4 • December 2020
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