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Reduction of enveloping algebras of low-rank groups

We find the generating function for group tensors contained in the enveloping algebra of each simple compact group of rank three or less. The generating function depends on dummy variables which carry, as exponents, the degrees and representation labels of the tensors; it suggests an integrity basis, a finite number of elementary tensors, in terms of which all can be expressed as stretched tensor products. We show how the generating functions for tensors in the enveloping algebra of SO(5) and SU(3) reduce when the tensors are acting on the basis of representations for which one of the Cartan labels vanish. The missing label problem in the reduction SO(5) (R-HOOK) SO(3) restricted to SO(5) representations of the type (0,(nu)) is considered; the eigenvalues and eigenvectors of a missing label operator are found up to (including) representation (0,12).

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.68555
Date January 1980
CreatorsCouture, Michel, 1949-
PublisherMcGill University
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Formatapplication/pdf
CoverageDoctor of Philosophy (Department of Physics)
RightsAll items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated.
Relationalephsysno: 000127598, proquestno: AAINK51918, Theses scanned by UMI/ProQuest.

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