Modular categories of types B,C and D

Details Modular categories of types B,C and D Modular categories of types B,C and D

2000-06-30

arxiv.org/abs/math/0006227v3

Mathematics

Quantum Algebra

32 pages, LaTeX with figures, Comment. Math. Helv. 2001

Scientific paper

We construct four series of modular categories from the two-variable Kauffman polynomial, without use of the representation theory of quantum groups at roots of unity. The specializations of this polynomial corresponding to quantum groups of types B, C and D produce series of pre-modular categories. One of them turns out to be modular and three others satisfy Brugui\`eres' modularization criterion. For these four series we compute the Verlinde formulas, and discuss spin and cohomological refinements.

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