The pattern calculus for tensor operators in quantum groups

An explicit algebraic evaluation is given for all q‐tensor operators (with unit norm) belonging to the quantum group U q ( u(n)) and having extremal operator shift patterns acting on arbitrary U q ( u(n)) irreps. These rather complicated results are shown to be easily comprehensible in terms of a di...

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Bibliographic Details
Published in:Journal of mathematical physics 1992-11, Vol.33 (11), p.3613-3635
Main Authors: Gould, Mark, Biedenharn, L. C.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Group theory
Mathematical methods in physics
Physics
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Summary:An explicit algebraic evaluation is given for all q‐tensor operators (with unit norm) belonging to the quantum group U q ( u(n)) and having extremal operator shift patterns acting on arbitrary U q ( u(n)) irreps. These rather complicated results are shown to be easily comprehensible in terms of a diagrammatic calculus of patterns. A more conceptual derivation of these results is discussed using fundamental properties of the q−6j coefficients.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.529909