Abstract
Three aspects of the SU(3) fusion coefficients are revisited: the generating polynomials of fusion coefficients are written explicitly; some curious identities generalizing the classical Freudenthal–de Vries formula are derived; and the properties of the fusion coefficients under conjugation of one of the factors, previously analyzed in the classical case, are extended to the affine algebra suˆ(3) at finite level.
Highlights
The aim of this paper is threefold: 1) Write generating functions for SU(3) fusion matrices and coefficients. 2) Use them to get general formulae for dimensions of spaces of essential paths on fusion graphs and derive identities generalizing the classical Freudenthal–de Vries formula. 3) Compare multiplicities for λ ⊗ μ and λ ⊗ μ.Along the way we discuss several other properties of fusion coefficients that do not seem to have been discussed elsewhere.[m1+; v1.232; Prn:13/06/2016; 9:43] P.2 (1-32)R
What we do here is to provide generating formulae for the fusion matrices themselves
Moving from an underlying SU(2) to an underlying SU(3) framework leads to several intriguing formulae that we present
Summary
The aim of this paper is threefold: 1) Write generating functions for SU(3) fusion matrices and coefficients. 2) Use them to get general formulae for dimensions of spaces of essential paths on fusion graphs and derive identities generalizing the classical Freudenthal–de Vries formula. 3) Compare multiplicities for λ ⊗ μ and λ ⊗ μ (provide a proof that was missing in our paper [1]). The aim of this paper is threefold: 1) Write generating functions for SU(3) fusion matrices and coefficients. 2) Use them to get general formulae for dimensions of spaces of essential paths on fusion graphs and derive identities generalizing the classical Freudenthal–de Vries formula. 3) Compare multiplicities for λ ⊗ μ and λ ⊗ μ (provide a proof that was missing in our paper [1]). The purpose of this paper is to make a modest homage to the memory of our distinguished colleague and great friend Raymond Stora. In scientific discussions Raymond was a listener second to none, with unsurpassable insight, critical sharpness and good humor. In scientific discussions Raymond was a listener second to none, with unsurpassable insight, critical sharpness and good humor. . . . We hope that he would have found entertaining the following mix of algebraic, geometric and group theoretical considerations, but surely, he would have stimulated us with witty comments and inspiring suggestions
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