Representations of tensor categories and Dynkin diagrams
| dc.creator | Etingof, Pavel | |
| dc.creator | Khovanov, Mikhail | |
| dc.date | 1994-08-13 | |
| dc.date | 1994-08-30 | |
| dc.date.accessioned | 2026-07-07T09:03:44Z | |
| dc.date.available | 2026-07-07T09:03:44Z | |
| dc.description | 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)}. | |
| dc.description | 10 pages; errors in indexation in the Clebsch-Gordan and truncated Clebsch-Gordan formulas are corrected | |
| dc.identifier | https://arxiv.org/abs/hep-th/9408078 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9408078 | |
| dc.identifier | Int.Math.Res.Not. 5 (1995) 235-247 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149123 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Representations of tensor categories and Dynkin diagrams | |
| dc.type | text |