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A braided fusion category is said to have Property F if the associated braid group representations factor through a finite group. We verify integral metaplectic modular categories have property F by showing these categories are group-theoretical. For the special case of integral categories [Formula: see text] with the fusion rules of [Formula: see text] we determine the finite group [Formula: see text] for which [Formula: see text] is braided equivalent to [Formula: see text]. In addition, we determine the associated classical link invariant, an evaluation of the 2-variable Kauffman polynomial at a point.
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Braided Zestings of Verlinde Modular Categories and Their Modular Data
Abstract Zesting of braided fusion categories is a procedure that can be used to obtain new modular categories from a modular category with non-trivial invertible objects. In this paper, we classify and construct all possible braided zesting data for modular categories associated with quantum groups at roots of unity. We produce closed formulas, based on the root system of the associated Lie algebra, for the modular data of these new modular categories.
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- Award ID(s):
- 2205962
- PAR ID:
- 10547489
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 405
- Issue:
- 10
- ISSN:
- 0010-3616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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