Modular categories of types B,C and D

Abstract

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.