Integral Metaplectic Modular Categories

Deaton, Adam; Gustafson, Paul; Mavrakis, Leslie; Rowell, Eric C.; Poltoratski, Sasha; Timmerman, Sydney; Warren, Benjamin; Zhang, Qing

doi:10.48550/arxiv.1901.04462

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2019

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“…those whose Frobenius-Perron dimension is a positive integer [5,6,8,14,17,27,34,36,37]. The family of weakly integral metaplectic modular tensor categories related to the representation theory of special orthogonal groups has received particular attention [2,11,24]. It is conjectured that weakly integral braided fusion categories are unique among braided fusion categories in that their associated braid group representations factor over a finite group [35].…”

Section: Introductionmentioning

confidence: 99%

Quadratic $d$-numbers

Schopieray

2019

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Here we constructively classify quadratic d-numbers: algebraic integers in quadratic number fields generating Galois-invariant ideals. We prove the subset thereof maximal among their Galois conjugates in absolute value is discrete in R. Our classification provides a characterization of those real quadratic fields containing a unit of norm -1 which is known to be equivalent to the existence of solutions to the negative Pell equation. The notion of a weakly quadratic fusion category is introduced whose Frobenius-Perron dimension necessarily lies in this discrete set. Factorization, divisibility, and boundedness results are proven for quadratic d-numbers allowing a systematic study of weakly quadratic fusion categories which constitute essentially all known examples of fusion categories having no known connection to classical representation theory.

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Section: Introductionmentioning

confidence: 99%

Quadratic $d$-numbers

Schopieray

2019

Preprint

View full text Add to dashboard Cite

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Integral Metaplectic Modular Categories

Cited by 1 publication

References 8 publications

Quadratic $d$-numbers

Quadratic $d$-numbers

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