Gelfand pairs admit an Iwasawa decomposition
Dynamical Systems
2019-05-09 v5 Functional Analysis
Group Theory
Abstract
Every Gelfand pair (G,K) admits a decomposition G=KP, where P<G is an amenable subgroup. In particular, the Furstenberg boundary of G is homogeneous. Applications include the complete classification of non-positively curved Gelfand pairs, relying on earlier joint work with Caprace, as well as a canonical family of pure spherical functions in the sense of Gelfand--Godement for general Gelfand pairs.
Cite
@article{arxiv.1902.09497,
title = {Gelfand pairs admit an Iwasawa decomposition},
author = {Nicolas Monod},
journal= {arXiv preprint arXiv:1902.09497},
year = {2019}
}