Integral metaplectic modular categories

被引：0

作者：

Deaton, Adam ^{[1
]}

Gustafson, Paul ^{[1
]}

Mavrakis, Leslie ^{[2
]}

Rowell, Eric C. ^{[1
]}

Poltoratski, Sasha ^{[3
]}

Timmerman, Sydney ^{[4
]}

Warren, Benjamin ^{[5
]}

Zhang, Qing ^{[1
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Seattle Pacific Univ, Dept Math, Seattle, WA 98119 USA

[3] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[4] Johns Hopkins Univ, Dept Phys & Astron, Baltimore, MD 21218 USA

[5] Swarthmore Coll, Dept Math & Stat, Swarthmore, PA 19081 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2020年 / 29卷 / 05期

关键词：

Group-theoretical braided fusion category; property F; link invariant; braid group representation;

D O I：

10.1142/S0218216520500327

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 C with the fusion rules of SO(8)(2) we determine the finite group G for which Rep(D(omega)G) is braided equivalent to Z(C). In addition, we determine the associated classical link invariant, an evaluation of the 2-variable Kauffman polynomial at a point.

引用

页数：9

共 50 条

[21] Integral Representations for the Class of Generalized Metaplectic Operators
Cordero, Elena
Nicola, Fabio
Rodino, Luigi
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2015, 21 (04) : 694 - 714
[22] Ribbon Abelian categories as modular categories
Lyubashenko, V
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 1996, 5 (03) : 311 - 403
[23] Modular categories are not determined by their modular data
Mignard, Michael
Schauenburg, Peter
LETTERS IN MATHEMATICAL PHYSICS, 2021, 111 (03)
[24] Modular categories are not determined by their modular data
Michaël Mignard
Peter Schauenburg
Letters in Mathematical Physics, 2021, 111
[25] Integral representations for metaplectic operators: energy localization problems
Oonincx, P
ter Morsche, H
ADVANCED SIGNAL PROCESSING ALGORITHMS, ARCHITECTURES, AND IMPLEMENTATIONS X, 2000, 4116 : 125 - 134
[26] On the structure of modular categories
Müger, M
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2003, 87 : 291 - 308
[27] Spin modular categories
Beliakova, Anna
Blanchet, Christian
Contreras, Eva
QUANTUM TOPOLOGY, 2017, 8 (03) : 459 - 504
[28] Weil Representation and Metaplectic Groups over an Integral Domain
Chinello, Gianmarco
Turchetti, Daniele
COMMUNICATIONS IN ALGEBRA, 2015, 43 (06) : 2388 - 2419
[29] On invariants of modular categories beyond modular data
Bonderson, Parsa
Delaney, Colleen
Galindo, Cesar
Rowell, Eric C.
Tran, Alan
Wang, Zhenghan
JOURNAL OF PURE AND APPLIED ALGEBRA, 2019, 223 (09) : 4065 - 4088
[30] On special L-values attached to metaplectic modular forms
Bouganis, Thanasis
MATHEMATISCHE ZEITSCHRIFT, 2018, 288 (3-4) : 725 - 740

← 1 2 3 4 5 →