## Journal of Mathematics of Kyoto University

### On lie algebras of K-invariant functions

#### Abstract

Let $G$ be a locally compact group and let $K$ be a compact subgroup of $Aut(G)$, the group of automorphisms of $G$. $(G,K)$ is a Gelfand pair if the algebra $L_{K}^{1}(G)$ of K-invariant integrable functions on $G$ is commutative under convolution. In this paper, we give some charactezations of this algebra in the nilpotent case, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in [1] and obtain a new criterion for Gelfand pairs.

#### Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 4 (2008), 847-855.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250271320

Digital Object Identifier
doi:10.1215/kjm/1250271320

Mathematical Reviews number (MathSciNet)
MR2513588

Zentralblatt MATH identifier
1170.43002

Subjects
Primary: 430A20 17B30: Solvable, nilpotent (super)algebras

#### Citation

Toure, Ibrahima; Kangni, Kinvi. On lie algebras of K-invariant functions. J. Math. Kyoto Univ. 48 (2008), no. 4, 847--855. doi:10.1215/kjm/1250271320. https://projecteuclid.org/euclid.kjm/1250271320