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AN EXTERNAL APPROACH TO UNITARY REPRESENTATIONS
, 1993
"... The principal ideas of harmonic analysis on a locally compact group G which is not necessarily compact or commutative were developed in the 1940s and early 1950s. In this theory, the role of the classical fundamental harmonics is played by the irreducible unitary representations of G. The set of all ..."
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Cited by 11 (1 self)
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The principal ideas of harmonic analysis on a locally compact group G which is not necessarily compact or commutative were developed in the 1940s and early 1950s. In this theory, the role of the classical fundamental harmonics is played by the irreducible unitary representations of G. The set
THE MOMENT MAPPING FOR UNITARY REPRESENTATIONS
 ANNALS OF GLOBAL ANALYSIS AND GEOMETRY VOL. 8, NO. 3 (1990), 299–313
, 1990
"... For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of analytic vectors the same construction is possible and leads ..."
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Cited by 7 (5 self)
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For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of analytic vectors the same construction is possible
Holomorphic extension of unitary representations
"... Let H be a complex Hilbert space and π: G → U(H) a continuous unitary representation of the Lie group G on H. In this note we will discuss the problem of extending π holomorphically to a complex manifold which carries the structure of a complex semigroup and which contains G as its group of units in ..."
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Let H be a complex Hilbert space and π: G → U(H) a continuous unitary representation of the Lie group G on H. In this note we will discuss the problem of extending π holomorphically to a complex manifold which carries the structure of a complex semigroup and which contains G as its group of units in
Branching Problems of Unitary Representations
 ICM 2002 · VOL. III · 1–3
, 2003
"... The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a noncompact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs discretely with finite multiplicity (admissible restrictions). Basic ..."
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Cited by 12 (8 self)
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The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a noncompact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs discretely with finite multiplicity (admissible restrictions
ON UNITARY REPRESENTABILITY OF TOPOLOGICAL GROUPS
, 2006
"... Abstract. We prove that the additive group (E ∗ , τk(E)) of an L∞Banach space E, with the topology τk(E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving tha ..."
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Cited by 2 (0 self)
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Abstract. We prove that the additive group (E ∗ , τk(E)) of an L∞Banach space E, with the topology τk(E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving
Unitary Representations of Lie Groups with . . .
, 1997
"... We consider the following class of unitary representations π of some (real) Lie group G which has a matched pair of symmetries described as follows: (i) Suppose G has a period2 automorphism τ, and that the Hilbert space H(π) carries a unitary operator J such that Jπ = (π ◦ τ)J (i.e., selfsimilarity ..."
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We consider the following class of unitary representations π of some (real) Lie group G which has a matched pair of symmetries described as follows: (i) Suppose G has a period2 automorphism τ, and that the Hilbert space H(π) carries a unitary operator J such that Jπ = (π ◦ τ)J (i
Unitary Representations Of Reductive Lie Groups
 ANNALS OF MATHEMATICS STUDIES
, 1987
"... One of the fundamental problems of abstract harmonic analysis is the determination of the irreducible unitary representations of simple Lie groups. After recalling why this problem is of interest, we discuss the present state of knowledge about it. In the language of Kirillov and Kostant, the pr ..."
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Cited by 49 (5 self)
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One of the fundamental problems of abstract harmonic analysis is the determination of the irreducible unitary representations of simple Lie groups. After recalling why this problem is of interest, we discuss the present state of knowledge about it. In the language of Kirillov and Kostant
A Langlands classification for unitary representations
, 1998
"... The Langlands classification theorem describes all admissible representations of a reductive group G in terms of the tempered representations of Levi subgroups of G. I will describe work with Susana SalamancaRiba that provides (conjecturally) a similar description of the unitary representation ..."
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Cited by 2 (1 self)
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The Langlands classification theorem describes all admissible representations of a reductive group G in terms of the tempered representations of Levi subgroups of G. I will describe work with Susana SalamancaRiba that provides (conjecturally) a similar description of the unitary
Results 1  10
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2,055