L p -Estimates for Matrix Coefficients of Irreducible Representations of Compact Groups

In this paper we consider matrix representations of compact groups over the field of the complex numbers. We shall deal mainly with finite groups.The Kronecker product of two irreducible representations σ1and σ2of a groupis in general a reducible representation of. The explicit reduction of such a product to irreducible representations σ3can be performed by means of a unitary matrix, the elements of which are called Wigner coefficients or Clebsch-Gordan coefficients [1; 25; 27].

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Locally compact groups whose conjugation representations satisfy a Kazhdan type property or have countable support

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410007239x ◽

1994 ◽

Vol 116 (1) ◽

pp. 79-97 ◽

Cited By ~ 1

Author(s):

Eberhard Kaniuth ◽

Annette Markfort

Keyword(s):

Modular Function ◽

Equivalence Classes ◽

Irreducible Representations ◽

Compact Groups ◽

Locally Compact ◽

Countable Support ◽

Type Property ◽

Invariant Means ◽

Image Position ◽

Conjugation Representation

For a locally compact group G with left Haar measure and modular function δ the conjugation representation γG of G on L2(G) is defined byf ∈ L2(G), x, y ∈ G. γG has been investigated recently (see [19, 20, 21, 24, 32, 35]). For semi-simple Lie groups, a related representation has been studied in [25]. γG is of interest not least because of its connection to questions on inner invariant means on L∞(G). In what follows suppγG denotes the support of γG in the dual space Ĝ, that is the closed subset of all equivalence classes of irreducible representations which are weakly contained in γG. The purpose of this paper is to establish relations between properties such as a variant of Kazhdan's property and discreteness or countability of supp γG and the structure of G.

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DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS

Glasgow Mathematical Journal ◽

10.1017/s0017089516000252 ◽

2016 ◽

Vol 59 (2) ◽

pp. 421-435 ◽

Cited By ~ 2

Author(s):

MAHMOOD ALAGHMANDAN ◽

MASSOUD AMINI

Keyword(s):

Representation Theory ◽

Finite Groups ◽

Dual Space ◽

Conjugacy Classes ◽

Irreducible Representations ◽

Compact Groups ◽

Dual Spaces ◽

Heisenberg Inequality

AbstractWe characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.

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On non-compact groups. IV. Some representations of widetilde{ SU } 4 ( NU 2 4 )

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1965.0204 ◽

1965 ◽

Vol 288 (1412) ◽

pp. 113-122 ◽

Cited By ~ 2

Keyword(s):

Compact Subgroup ◽

Energy Operator ◽

Rotation Group ◽

Positive Definite ◽

Elementary Particles ◽

Unitary Representations ◽

Irreducible Representations ◽

Compact Groups ◽

The Relationship ◽

Real Forms

It has been suggested that certain non-compact groups, among them widetilde{ SU } 12 , may be relevant for the theory of elementary particles. In that case it would be of interest to study their unitary representations. As a beginning we study the non-compact subgroup widetilde{ SU } 4 , of widetilde{ SU } 12 . We find that among several non-compact real forms of SU 4 , only that which is isomorphic to the rotation group R 2,4 is of interest. For this group we determine all the unitary irreducible representations for which the energy operator has a positive definite spectrum. Then we study the relationship between these representations and those of the Poincare group.

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