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27
A local PeterWeyl theorem
 Trans. Amer. Math. Soc
"... Abstract. An Ad K invariant inner product on the Lie algebra of a compact connected Lie group K extends to a Hermitian inner product on the Lie algebra of the complexified Lie group Kc. The LaplaceBeltrami operator, ∆, on Kc induced by the Hermitian inner product determines, for each number a>0, ..."
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Cited by 3 (0 self)
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Abstract. An Ad K invariant inner product on the Lie algebra of a compact connected Lie group K extends to a Hermitian inner product on the Lie algebra of the complexified Lie group Kc. The LaplaceBeltrami operator, ∆, on Kc induced by the Hermitian inner product determines, for each number a>0, a Green’s function ra by means of the identity (a 2 − ∆/4) −1 = ra∗. The Hilbert space of holomorphic functions on Kc which are square integrable with respect to ra(x)dx is shown to be finite dimensional. It is spanned by the holomorphic extensions of the matrix elements of those irreducible representations of K whose Casimir operator is appropriately related to a. 1.
THE HOLOMORPHIC PETERWEYL THEOREM AND THE BLATTNERKOSTANTSTERNBERG PAIRING
, 2006
"... Abstract. Let K be a compact Lie group, endowed with a biinvariant Riemannian metric, which we denote by κ. The complexification KC of K inherits a Kähler structure having twice the kinetic energy of the metric as its potential; let ε denote the symplectic volume form. Left and right translation tu ..."
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Cited by 4 (3 self)
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interpretation, this parameter amounts to Planck’s constant We establish the statement of the PeterWeyl theorem for the Hilbert space HL 2 (K C,e −κ/t ηε) to the effect that (i) HL 2 (K C, e −κ/t ηε) contains the vector space of representative functions on K C as a dense subspace and that (ii) the assignment
KIRILLOV’S CHARACTER FORMULA, THE HOLOMORPHIC PETERWEYL THEOREM, AND THE BLATTNERKOSTANTSTERNBERG PAIRING
, 2007
"... Abstract. Let K be a compact Lie group, endowed with a biinvariant Riemannian metric, which we denote by κ. The complexification KC of K inherits a Kähler structure having twice the kinetic energy of the metric as its potential; let ε denote the symplectic volume form. Left and right translation tu ..."
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Cited by 7 (2 self)
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interpretation, this parameter amounts to Planck’s constant We establish the statement of the PeterWeyl theorem for the Hilbert space HL 2 (K C,e −κ/t ηε) to the effect that (i) HL 2 (K C, e −κ/t ηε) contains the vector space of representative functions on K C as a dense subspace and that (ii) the assignment
CQG algebras: a direct algebraic approach to compact quantum groups
, 1994
"... The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the PeterWeyl theorem for CQG algebras and the existence of a unique positive definite Haar functional on any CQG algebra are established. It is shown that ..."
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Cited by 40 (1 self)
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The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the PeterWeyl theorem for CQG algebras and the existence of a unique positive definite Haar functional on any CQG algebra are established. It is shown
Continuous representations of groupoids
, 2007
"... Abstract. We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects, using several examples. We present a palette of results, including, among others: a comparison of the different notions of continuity for r ..."
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Cited by 14 (0 self)
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for representations, a description of the representations of families of groups, and a version of the PeterWeyl theorem for groupoids. 1.
LÉVY PROCESSES AND FOURIER ANALYSIS ON COMPACT LIE GROUPS
, 2004
"... We study the Fourier expansion of the distribution density of a Lévy process in a compact Lie group based on the Peter–Weyl theorem. 1. Introduction. Let G be a Lie group with identity element e and of dimension d. A stochastic process gt in G, with right continuous paths having left limits, is call ..."
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Cited by 8 (0 self)
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We study the Fourier expansion of the distribution density of a Lévy process in a compact Lie group based on the Peter–Weyl theorem. 1. Introduction. Let G be a Lie group with identity element e and of dimension d. A stochastic process gt in G, with right continuous paths having left limits
By
, 1970
"... The concept of a topological group arose originally in connection with the study of continuous transformation groups. Later it became apparent that it was unnecessary to regard the group as a group of transformations. Today it is an area of much interest to mathematicians. The purpose of this paper ..."
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is tc develop an invariant integral for a compact topological group and, then to use that integral to prove the fundamental PeterWeyl Theorem. The first chapter of this paper will investigate some properties of compact topological groups and the continuous realvalued functions defined on such groups
Dolbeault Cohomology of G/(P, P)
 MATH. Z. 230, 595–602 (1999)
, 1999
"... Let G be a complex connected semisimple Lie group, with parabolic subgroup P. Let (P; P) be its commutator subgroup. The generalized BorelWeil theorem on flag manifolds has an analogous result on the Dolbeault cohomology H0;q(G=(P; P)). Consequently, the dimension ofH0;q(G=(P; P)) is either 0 or1 ..."
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1. In this paper, we show that theDolbeault operator @ has closed image, and apply the PeterWeyl theorem to show how q determines the value 0 or 1. For the case when P is maximal, we apply our result to compute the Dolbeault cohomology of certain examples, such as the punctured determinant bundle
Results 1  10
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27