Principal Gelfand pairs
نویسندگان
چکیده
منابع مشابه
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...
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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.
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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
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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...
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The classical theory of Gelfand pairs has found a wide range of applications, ranging from harmonic analysis on Riemannian symmetric spaces to coding theory. Here we discuss a generalization of this theory, due to Gelfand-Kazhdan, and Bernstein, which was developed to study the representation theory of p-adic groups. We also present some recent number-theoretic results, on local e-factors and o...
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ژورنال
عنوان ژورنال: Transformation Groups
سال: 2006
ISSN: 1083-4362,1531-586X
DOI: 10.1007/s00031-005-1110-9