A generalized Gelfand pair attached to 3-step nilpotent Lie group
Functional Analysis
2020-05-14 v1
Abstract
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 (KnN,N) is a Gelfand pair then N is at most 2-step nilpotent Lie group. The notion of Gelfand pair was generalized when K is a non-compact group. In this work, we give an example of a 3-step nilpotent Lie group and a non-compact subgroup K of Aut(N) such that (K nN,N) is a generalized Gelfand pair.
Keywords
Cite
@article{arxiv.2005.06362,
title = {A generalized Gelfand pair attached to 3-step nilpotent Lie group},
author = {Andrea L. Gallo and Linda V. Saal},
journal= {arXiv preprint arXiv:2005.06362},
year = {2020}
}