Generalized Gelfand Pairs Associated to m-Step Nilpotent Lie Groups

Let N be a nilpotent Lie group and K a compact subgroup of the automorphism group Aut ( N ) of N . It is well known that if ( K ⋉ N , K ) is a Gelfand pair then N is at most 2-step nilpotent Lie group. This notion has been generalized to non-compact groups K . In this work, we exhibit a family ( K m...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of geometric analysis 2023-02, Vol.33 (2), Article 54
Main Authors: Campos, Silvina, García, José, Saal, Linda
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Automorphisms
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Lie groups
Mathematics
Mathematics and Statistics
Subgroups
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let N be a nilpotent Lie group and K a compact subgroup of the automorphism group Aut ( N ) of N . It is well known that if ( K ⋉ N , K ) is a Gelfand pair then N is at most 2-step nilpotent Lie group. This notion has been generalized to non-compact groups K . In this work, we exhibit a family ( K m ⋉ N m , K m ) of generalized Gelfand pairs, where N m is a m + 2 -step nilpotent Lie group and K m is isomorphic to R m + 1 .
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-01099-4