Representations of tensor categories and Dynkin diagrams

Details Representations of tensor categories and Dynkin diagrams Representations of tensor categories and Dynkin diagrams

1994-08-13

arxiv.org/abs/hep-th/9408078v2

Int.Math.Res.Not. 5 (1995) 235-247

Physics

High Energy Physics

High Energy Physics - Theory

10 pages; errors in indexation in the Clebsch-Gordan and truncated Clebsch-Gordan formulas are corrected

Scientific paper

In this note we illustrate by a few examples the general principle: interesting algebras and representations defined over Z_+ come from category theory, and are best understood when their categorical origination has been discovered. We show that indecomposable Z_+-representations of the character ring of SU(2) satisfying certain conditions correspond to affine and infinite Dynkin diagrams with loops. We also show that irreducible Z_+-representations of the Verlinde algebra (the character ring of the quantum group SU(2)_q, where q is a root of unity), satisfying similar conditions correspond to usual (non-affine) Dynkin diagrams with loops. Conjecturedly, the last result is related to the ADE classification of conformal field theories with the chiral algebra \hat{sl(2)}.

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