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DISCRETE SYMMETRY OPERATORS FOR REDUCTIVE LIE GROUPS
In this paper a description is given of a family of homomorphisms of elementary G-modules (where G is a semisimple connected Lie group) called discrete symmetry operators. Groups of rank 1 areExpand
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HARMONIC ANALYSIS OF FUNCTIONS ON SEMISIMPLE LIE GROUPS. II
A theory of harmonic analysis is developed for the class of functions (fundamental and generalized) with compact support on an arbitrary semisimple complex connected Lie group. Duality theorems areExpand
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The Analysis of Irreducibility in the Class of Elementary Representations of a Complex Semisimple Lie Group
We study the class of "elementary" representations for a complex semisimple Lie group, obtained by analytic continuation from the Gel'fand-Naĭmark "fundamental series." We establish necessary andExpand
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OPERATIONAL CALCULUS ON A COMPLEX SEMISIMPLE LIE GROUP
For every complex semisimple Lie algebra we construct a so-called operational calculus, which consists in the isomorphic embedding of along with its associative hull into a certain algebra ofExpand
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CLASSIFICATION OF EXTREMALLY IRREDUCIBLE AND NORMALLY IRREDUCIBLE REPRESENTATIONS OF SEMISIMPLE COMPLEX CONNECTED LIE GROUPS
A new concept of "extremal irreducibility" for representations of Lie groups in separable locally convex spaces is introduced. All extremally irreducible representations of semisimple complex LieExpand
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A DESCRIPTION OF THE QUASI-SIMPLE IRREDUCIBLE REPRESENTATIONS OF THE GROUPS U(n, 1) AND Spin(n, 1)
This article deals with a family of elementary G-modules E(σ), where G is either one of the groups U(n,1), with n > 1, or one of the groups Spin(n, 1), with n > 2. A description is given of all ofExpand
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Fifteen Papers on Analysis
DESCRIPTION OF THE COMPLETELY IRREDUCIBLE REPRESENTATIONS OF A COMPLEX SEMISIMPLE LIE GROUP
We give a complete description (up to a certain equivalence) of all the completely irreducible representations of a connected complex semisimple Lie group in separated complete (at leastExpand
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