Generalized Whittaker functions for degenerate principal series of \(\mathrm{GL}(n, \mathbb{R})\)
type: Item
instance of: scholarly article
title: Generalized Whittaker functions for degenerate principal series of \(\mathrm{GL}(n, \mathbb{R})\)
zbMATH Open document ID: 1259.22011
DOI: 10.2977/PRIMS/88
author: Kazuki Hiroe
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2013-01-17T00:00:00Z
review text: The author studies generalized Whittaker functions of degenerate principle series of \(\mathrm{GL}(n, \mathbb{R})\). The first main result is a general characterization of the spaces of corresponding class one generalized Whittaker functions by an explicit system of differential operators. Using this result, the author presents detailed calculations in the case of the group \(\mathrm{GL}(4, \mathbb{R})\), considering degenerate principal series induced from different maximal parabolic subgroups. We emphasize that previously made results were mainly related to generalized principal series induced from a maximal parabolic subgroup \(P_{1, n}\) fixing the unit vector \(e_{n} = (0, \dotsc, 0, 1)\). In the considered case, the author examines the dimension of the spaces of class one generalized Whittaker functions, finds their bases in terms of hypergeometric functions in one and two variables and proves a corresponding multiplicity one theorem.
reviewed by: Ivan Matić
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 6126564
zbMATH Keywords: generalized Whittaker model
zbMATH Keywords: general linear group
zbMATH Keywords: degenerate principal series
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: multiplicity one theorems
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.2977/prims/88
OpenAlex ID: W2145975885
description: scientific article; zbMATH DE number 6126564