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The center of the extended Haagerup subfactor has 22 simple objects
Abstract
We explain a technique for discovering the number of simple objects in , the center of a fusion category , as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring and the dimension function . In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165.] to compute the full modular data. This is the published version of arXiv:1404.3955.
AMSC: 18D05, 18D10, 46L37, 57R56, 81T40
References
- 1. , Constructing the extended Haagerup planar algebra, Acta Math. 209(1) (2012) 29–82, arXiv:0909.4099, MR2979509, doi: 10.1007/s11511-012-0081-7. Crossref, ISI, Google Scholar
- 2. , Some properties of finite-dimensional semisimple Hopf algebras, Math. Res. Lett. 5(1–2) (1998) 191–197, MR1617921, doi: 10.4310/MRL.1998.v5.n2.a5. Crossref, ISI, Google Scholar
- 3. , On fusion categories, Ann. of Math. (2) 162(2) (2005) 581–642, arXiv:math.QA/0203060, MR2183279, doi: 10.4007/annals.2005.162.581. Crossref, ISI, Google Scholar
- 4. P. Grossman and M. Izumi, Quantum doubles of generalized Haagerup subfactors and their orbifolds preprint (2015), arXiv:1501.07679. Google Scholar
- 5. T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor preprint (2016), arXiv:1606.07165. Google Scholar
- 6. , Subfactors of index less than 5, Part 3: Quadruple points, Comm. Math. Phys. 316(2) (2012) 531–554, arXiv:1109.3190, MR2993924, doi: 10.1007/s00220-012-1472-5. Crossref, ISI, Google Scholar
- 7. , The structure of sectors associated with Longo-Rehren inclusions. II. Examples, Rev. Math. Phys. 13(5) (2001) 603–674, MR1832764, doi: 10.1142/S0129055X01000818. Link, ISI, Google Scholar
- 8. S. Morrison, Provide a citation for the “spine lemma”? MathOverflow (2013), http://mathoverflow.net/q/142456 (version: 2013-09-19). Google Scholar
- 9. , Constructing spoke subfactors using the jellyfish algorithm, Trans. Amer. Math. Soc. 367(5) (2015) 3257–3298, arXiv:1208.3637, MR3314808, doi: 10.1090/S0002-9947-2014-06109-6. Crossref, ISI, Google Scholar
- 10. , Classification of subfactors of index less than 5, Part 2: Triple points, Internat. J. Math. 23(3) (2012) 1250016, arXiv:1007.2240, MR2902285, doi: 10.1142/S0129167X11007586. Link, ISI, Google Scholar
- 11. , Subfactors of index less than 5, Part 1: The principal graph odometer, Comm. Math. Phys. 312(1) (2012) 1–35, arXiv:1007.1730, MR2914056, doi: 10.1007/s00220-012-1426-y. Crossref, ISI, Google Scholar
- 12. , On formal codegrees of fusion categories, Math. Res. Lett. 16(5) (2009) 895–901, arXiv:0810.3242, MR 2576705. Crossref, ISI, Google Scholar
- 13. , Subfactors of index less than 5, Part 4: Vines, Internat. J. Math. 23(3) (2012) 1250017, arXiv:1010.3797, MR2902286, doi: 10.1142/S0129167X11007641. Link, ISI, Google Scholar
