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Modular categories of types B, C and D


Beliakova, A; Blanchet, C (2001). Modular categories of types B, C and D. Commentarii Mathematici Helvetici, 76(3):467-500.

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 Bruguières’ modularization criterion. For these four series we compute the Verlinde formulas, and discuss spin and cohomological refinements.

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 Bruguières’ modularization criterion. For these four series we compute the Verlinde formulas, and discuss spin and cohomological refinements.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Modular category, modular functor, TQFT, 3-manifold, quantum invariants, Verlinde formula
Language:English
Date:2001
Deposited On:14 Apr 2010 07:01
Last Modified:05 Apr 2016 13:25
Publisher:Birkhäuser
ISSN:0010-2571
Publisher DOI:https://doi.org/10.1007/PL00000385

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