Quantum Groups at Roots of Unity and Modularity

Details Quantum Groups at Roots of Unity and Modularity Quantum Groups at Roots of Unity and Modularity

2003-08-28

arxiv.org/abs/math/0308281v2

Mathematics

Quantum Algebra

30 pages, AMS LaTeX typo fixed in chart in introduction

Scientific paper

For each compact, simple, simply-connected Lie group and each integer level we construct a modular tensor category from a quotient of a certain subcategory of the category of representations of the corresponding quantum group. We determine when at fractional levels the corresponding category is modular. We also give a quantum version of the Racah formula for the decomposition of the tensor product. This work relies on developing the basic representation theory of quantum groups at roots of unity, including Harish-Chandra's Theorem. It generalizes previous work which applied only to fractional levels or only to the projective form of the group.

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