Commutative avatars of representations of semisimple Lie groups. [PDF]
Proc Natl Acad Sci U S AHere 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 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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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.
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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
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APPLICATIONS OF THE RADON TRANSFORM TO REPRESENTATIONS OF SEMISIMPLE LIE GROUPS [PDF]
Proceedings of the National Academy of Sciences, 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 ...
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Harish-Chandra Highest Weight Representations of Semisimple Lie Algebras and Lie Groups
Journal of Lie Theory, 2023 In this expository paper we describe the theory of Harish-Chandra highest weight representations and their explicit geometric realizations.
Fioresi R., Varadarajan V. S.
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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 $U(2,2)$.
Vershik, A. M., Graev, M. I.
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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
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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 (
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Relatively dominated representations from eigenvalue gaps and limit maps. [PDF]
Geom Dedic, 2023 Zhu F.
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