Representations of tensor categories and Dynkin diagrams

dc.creatorEtingof, Pavel
dc.creatorKhovanov, Mikhail
dc.date1994-08-13
dc.date1994-08-30
dc.date.accessioned2026-07-07T09:03:44Z
dc.date.available2026-07-07T09:03:44Z
dc.descriptionIn 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)}.
dc.description10 pages; errors in indexation in the Clebsch-Gordan and truncated Clebsch-Gordan formulas are corrected
dc.identifierhttps://arxiv.org/abs/hep-th/9408078
dc.identifierhttp://arxiv.org/abs/hep-th/9408078
dc.identifierInt.Math.Res.Not. 5 (1995) 235-247
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149123
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleRepresentations of tensor categories and Dynkin diagrams
dc.typetext

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