A Cartan decomposition for Gelfand pairs and induction of spherical functions
type: Item
instance of: scholarly article
title: A Cartan decomposition for Gelfand pairs and induction of spherical functions
author: Yuichiro Tanaka
published in: Journal of the Mathematical Society of Japan
publication date: 2022-10-27T00:00:00Z
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 7608351
zbMATH Keywords: Cartan decomposition
zbMATH Keywords: Gelfand pair
zbMATH Keywords: Lie group
zbMATH Keywords: spherical function
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/85588558
OpenAlex ID: W4210409052
cites work: On Lie algebra decompositions, related to spherical homogeneous spaces
cites work: Weakly symmetric spaces and spherical varieties
cites work: Bounded \(K\)-spherical functions on Heisenberg groups
cites work: Espaces homogènes sphériques. (Spherical homogeneous spaces)
cites work: Polar Coordinates Induced by Actions of Compact Lie Groups
cites work: Plancherel theory for real spherical spaces: Construction of the Bernstein morphisms
cites work: Q3897665
cites work: Q4520850
cites work: Q4301588
cites work: Invariant differential operators on spherical homogeneous spaces with overgroups
cites work: The plancherel formula for group extensions II
cites work: The asymptotic behavior of invariant collective motion
cites work: Classification of reductive real spherical pairs. I: The simple case
cites work: Discrete decomposability of restriction of \(A_{\mathfrak q}(\lambda)\) with respect to reductive subgroups and its applications
cites work: Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups
cites work: Global analysis by hidden symmetry
cites work: Finite multiplicity theorems for induction and restriction
cites work: Q4186561
cites work: Holomorphic extensions of representations. I: Automorphic functions
cites work: Imprimitivity for Representations of Locally Compact Groups I
cites work: On a conjecture of Montgomery
cites work: An infinitesimal characterization of Gel′fand pairs
cites work: Homogeneous domains on flag manifolds and spherical subgroups of semisimple Lie groups
cites work: Q3994337
cites work: Q4004200
cites work: Q5754567
DOI: 10.2969/JMSJ/85588558
Recommended article: Spherical functions for Gelfand pairs associated with compact groupoids
Recommended article: Spherical functions for Gelfand pairs of complex reflection groups
Recommended article: Generating functions for the spherical functions on some classical Gelfand pairs
Recommended article: Generating functions and integral representations for the spherical functions on some classical Gelfand pairs
Recommended article: A Cartan decomposition for a reductive real spherical homogeneous space
Recommended article: Generating function for the spherical functions on a Gelfand pair of exceptional type
Recommended article: Spherical generalized functions induced on \(G_{\mathbb{C}}/G_{\mathbb{R}}\) and applications
Recommended article: Nilpotent Gelfand pairs and Schwartz extensions of spherical transforms via quotient pairs
Recommended article: Q5001444
Recommended article: A Cartan decomposition for non-symmetric reductive spherical pairs of rank-one type and its application to visible actions
description: scientific article; zbMATH DE number 7608351