Fusion rules and the Patera-Sharp generating-function method
L. Begin, C. Cummins, P. Mathieu, M.A. Walton
TL;DR
This paper reviews fusion rules and the Patera-Sharp generating-function method, explaining key concepts like the Kac-Walton formula and fusion bases with simple examples, highlighting their mathematical structure and applications.
Contribution
It provides an accessible review of fusion rule concepts and the Patera-Sharp generating-function approach, emphasizing elementary explanations and illustrative examples.
Findings
Clarifies the Patera-Sharp generating-function method
Explains fusion rules and related concepts with simple examples
Summarizes the Kac-Walton formula and fusion bases
Abstract
We review some contributions on fusion rules that were inspired by the work of Sharp, in particular, the generating-function method for tensor-product coefficients that he developed with Patera. We also review the Kac-Walton formula, the concepts of threshold level, fusion elementary couplings, fusion generating functions and fusion bases. We try to keep the presentation elementary and exemplify each concept with the simple case.
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Taxonomy
TopicsOptics and Image Analysis