Representations of tensor categories and Dynkin diagrams
Abstract
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 (nonaffine) 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)}.
 Publication:

arXiv eprints
 Pub Date:
 August 1994
 arXiv:
 arXiv:hepth/9408078
 Bibcode:
 1994hep.th....8078E
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 10 pages