An application of the duality between representations and classes

Vries, E. de; Zanten, A.J. van

doi:10.1016/0031-8914(70)90082-0

Cited by 5 publications

(2 citation statements)

References 2 publications

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“…Another approach is to build up1 an appropriate generalization from the other nodes. is a special case (A = 0), and since it is a class function it may be thought of as a class/IRREP duality transformation [21] of which the duality transformation X? (pr) is a generalization.…”

Section: Definitionsmentioning

confidence: 99%

“…Class sum theory [18,191 and the algebra of group representations give rise to a fairly extensive duality (e.g., Refs. [20][21][22] with conventional theory, and others [23-271, for example, have discussed the related topic of new irreducible tensors in the group algebra. These methods have given insight, for example, into the generalization of the projection operators which have wide application (e.g., Lowdin [28]).…”

Section: Introductionmentioning

confidence: 99%

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Diagram approach to group algebraic methods

Black

Stedman

1982

Int J of Quantum Chemistry

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Class sum theory, the duality with IRREP methods and tensor operators in the group algebra are discussed by generalizing the diagrammatic approach of conventional IRREP theory to include group label manipulation. Concepts such as invariant nodes and Jucys-Levinson-Vanagas reduction theorems generalize straightforwardly. The results are capable of unique simplification for certain nodes, when the group rearrangement theorem is useable or when a class sum is performed. A duality transformation (between IRREP-partner and class-element labels) emerges as an important concept.

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Section: Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diagram approach to group algebraic methods

Black

Stedman

1982

Int J of Quantum Chemistry

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Projective character tables and Opechowski's theorem

Backhouse

1973

Physica

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Tensor operators of finite groups

Zanten

Vries

1973

Journal of Mathematical Physics

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Irreducible tensor operators of a finite group G are discussed as elements of the group algebras of G⊗n (n=1,2,3,…). Formulas are given for the number of times that an irreducible tensor operator of a certain rank can be constructed in these algebras and more specifically how often they can be constructed from the elements of a fixed class of conjugate elements in G⊗n (n=1,2,3,…). Some of results are interpreted in the framework of the duality between classes and irreducible representations in finite groups.

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An application of the duality between representations and classes

Cited by 5 publications

References 2 publications

Diagram approach to group algebraic methods

Diagram approach to group algebraic methods

Projective character tables and Opechowski's theorem

Tensor operators of finite groups

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