Results 121 to 130 of about 261 (163)

Representations of Semisimple Lie Groups

2010
The purpose of these lectures is to give an elementary introduction to some basic topics in the theory of representations of semisimple Lie groups. Within harmonic analysis I have limited myself to a special topic which is now fairly well-developed, namely Fourier analysis of spherical functions.
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On the Unitarized Adjoint Representation of a Semisimple Lie Group II

Canadian Journal of Mathematics, 1977
Let G be a connected semisimple Lie group with Lie algebra . Lebesgue measure on is invariant under the adjoint action of G; and so there is a natural unitary representation TG of G on L2 given ...
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On the tensor product of representations of semisimple Lie groups

Letters in Mathematical Physics, 1974
The problem of the decomposition of the tensor product of finite and infinite representations of a complex semigroup of a Lie group is examined by using the theory of characters of completely irreducible representations. A theorem is proved which indicates that completely irreducible representations enter into the expansion of the tensor product of a ...
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Representation and differential geometry of the semisimple Lie groups

Journal of Mathematical Physics, 1974
A systematic method is presented whereby any compact Lie group of n-real parameters is dealt with from an infinitesimal approach with the representative matrix method based on a group of inner automorphisms suggested in a previous paper. The group manifold, defined in terms of a metric of group parameters, is identified as a Riemannian one in which ...
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Some Properties of Square-Integrable Representations of Semisimple Lie Groups

The Annals of Mathematics, 1975
In the theory of irreducible representations of a compact Lie group, the formula for the multiplicity of a weight and the so-called theorem of the highest weight are among the most important results. At least conjecturally, both of these statements have analogues for the discrete series of representations of a semisimple Lie group. Let G be a connected,
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Representations of Semisimple Lie Groups and Their Matrix Elements

1992
One of fundamental results of the theory of finite dimensional representations is the following theorem (see, for example, reference [58] of the first volume).
N. Ja. Vilenkin, A. U. Klimyk
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Index theorems and dicrete series representations of semisimple lie groups

Annals of Global Analysis and Geometry, 1983
Let \((G,K)\) and \((U,K)\) be dual Riemannian symmetric pairs, of the non-compact and the compact type, respectively. Suppose that the set \(\widehat G_ d\) of discrete series representations in \(\widehat G\) is non-empty. Let \(\mathfrak g=\mathfrak k+\mathfrak p\) be the Cartan decomposition for the Lie algebra \(\mathfrak g\) of \(G\).
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Representations of complex semisimple Lie groups and their real forms

1992
All the Lie algebras and Lie groups considered in this chapter are finite-dimensional; sometimes without mentioning this specifically we confine ourselves to a reductive Lie group, i.e., to a direct product of a simple group by a 1-dimensional center.
A. N. Leznov, M. V. Saveliev
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On the Isomorphism and Diffeomorphism of Compact Semisimple Lie Groups

Mathematical Notes, 2022
V V Gorbatsevich, Gorbatsevich V V
exaly  

Infinitesimal Theory of Representations of Semisimple Lie Groups

1980
For any locally compact topological group G satisfying the second axiom of countability, let ℰ(G) be the set of all equivalence classes of irreducible unitary representations of G. Among the central goals of representation theory have been, first of all, to get a good understanding of the structure of ℰ(G); and secondly, once this is done, to do ...
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