On generalized Gelfand pairs

Gelfand pairs

Let K ⊂ G be a compact subgroup of a real Lie group G. Denote by D(X) thealgebra of G-invariant differential operators on the homogeneous space X = G/K. ThenX is called commutative or the pair (G,K) is called a Gelfand pair if the algebra D(X)is commutative. Symmetric Riemannian homogeneous spaces introduced by Élie Cartanand weakly symmetric homogeneous spaces introduced by Sel...

Gelfand Pairs and Spherical Functions

This is a summary of the lectures delivered on Special Functions and Linear Representation of Lie Groups at the NSF-CBMS Research Conference at East Carolina University in March 5-9, 1979. The entire lectures will be published by the American Mathematical Society as a conference monograph in Mathematics.

The Uncertainty Principle for Gelfand Pairs

We extend the classical Uncertainty Principle to the context of Gelfand pairs. The Gelfand pair setting includes riemannian symmetric spaces, compact topological groups, and locally compact abelian groups. If the locally compact abelian group is Rn we recover a sharp form of the classical Heisenberg uncertainty principle. Section

Gelfand pairs associated with finite Heisenberg groups

A topological group G together with a compact subgroup K are said to form a Gelfand pair if the set L1(K\G/K) of K-bi-invariant integrable functions on G is a commutative algebra under convolution. The situation where G and K are Lie groups has been the focus of extensive and ongoing investigation. Riemannian symmetric spaces G/K furnish the most widely studied and best understood examples. ([H...

On Gelfand pairs associated with nilpotent Lie groups