Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On Gel′fand pairs associated with solvable Lie groups


Authors: Chal Benson, Joe Jenkins and Gail Ratcliff
Journal: Trans. Amer. Math. Soc. 321 (1990), 85-116
MSC: Primary 22E25; Secondary 22D25, 43A20
DOI: https://doi.org/10.1090/S0002-9947-1990-1000329-0
MathSciNet review: 1000329
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be a locally compact group, and let $K$ be a compact subgroup of ${\operatorname {Aut}}(G)$, the group of automorphisms of $G$. There is a natural action of $K$ on the convolution algebra ${L^1}(G)$, and we denote by $L_K^1(G)$ the subalgebra of those elements in ${L^1}(G)$ that are invariant under this action. The pair $(K,G)$ is called a Gelfand pair if $L_K^1(G)$ is commutative. In this paper we consider the case where $G$ is a connected, simply connected solvable Lie group and $K \subseteq {\operatorname {Aut}}(G)$ is a compact, connected group. We characterize such Gelfand pairs $(K,G)$, and determine a moduli space for the associated $K$-spherical functions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E25, 22D25, 43A20

Retrieve articles in all journals with MSC: 22E25, 22D25, 43A20


Additional Information

Article copyright: © Copyright 1990 American Mathematical Society