Quantum Groups at Roots of Unity and Modularity

2003/08/28 by Stephen Sawin, Sawin, Stephen F. · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.math/0308281

Abstract

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.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• Reconstruction of tensor categories of type G₂

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