Results 1 to 10 of about 18,865 (173)

Commutative avatars of representations of semisimple Lie groups. [PDF]

Proc Natl Acad Sci U S A
Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are commutative finite flat algebras over the cohomology of the classifying space of the group. They are isomorphic with the equivariant
Hausel T.
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Classification of irreducible tempered representations of semisimple Lie groups. [PDF]

Proc Natl Acad Sci U S A, 1976
For each connected real semisimple matrix group, one obtains a constructive list of the irreducible tempered unitary representations and their characters. These irreducible representations all turn out to be instances of a more general kind of representation, here called basic.
Knapp AW, Zuckerman G.
europepmc   +7 more sources

Classification of the irreducible representations of semisimple Lie groups. [PDF]

Proc Natl Acad Sci U S A, 1977
We obtain a classification of the irreducible (nonunitary) representations of a connected semisimple Lie group G , in terms of their restriction to a maximal compact subgroup K of G .
Vogan DA.
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Applications of the radon transform to representations of semisimple lie groups. [PDF]

Proc Natl Acad Sci U S A, 1969
From the point of view of the duality between points and horocycles in a symmetric space, the counterparts to the spherical functions on the symmetric space are the conical distributions on the manifold of horocycles. While the conical functions are closely related to certain finite-dimensional representations of semisimple Lie groups, in the present ...
Helgason S.
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Square Integrable Representations of Semisimple Lie Groups [PDF]

Transactions of the American Mathematical Society, 1974
Let D be a bounded symmetric domain. Let G be the universal covering group of the identity component A 0 ( D ) {A_0}(D) of the group of all holomorphic diffeomorphisms of D onto itself. In this case, any G-homogeneous vector bundle E →
Juan Tirao
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Homogeneous complex manifolds and representations of semisimple lie groups. [PDF]

Proc Natl Acad Sci U S A, 1968
Schmid W.
europepmc   +7 more sources

Primitive stable representations in higher rank semisimple Lie groups [PDF]

Revista Matemática Complutense, 2020
We add some details concerning Corollary 1.6, revise the proof of Proposition 5.3 and correct ...
Inkang Kim, Sungwoon Kim
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Spectra in Representations of Semisimple Lie Groups [PDF]

Proceedings of the American Mathematical Society, 1973
The spectrum of the infinitesimal generator of a one-parameter group of unitary operators arising from a representation of a semisimple Lie group is determined. The support of the spectral measure depends only on whether the group is a group of automorphisms of a bounded symmetric domain. 1. Let [I be a (strongly) continuous unitary representation of a
Sidney C. Scull
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Intertwining Operators into Cohomology Representations for Semisimple Lie Groups

Journal of Functional Analysis, 1997
One approach to constructing unitary representations for semisimple Lie groups utilizes analytic cohomology on open orbits of generalized flag manifolds. This work gives explicit formulas for harmonic cocycles associated to certain holomorphic homogeneous vector bundles, extending previous results of the author (Intertwining operators into cohomology ...
Robert Donley, Robert Donley
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Cohomology in nonunitary representations of semisimple Lie groups (the group U(2, 2)) [PDF]

Functional Analysis and Its Applications, 2014
We suggest a method of constructing special nonunitary representations of semisimple Lie groups using representations of Iwasawa subgroups. As a typical example, we study the group $U(2,2)$.
Anatoly Vershik, M. I. Graev
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