## View abstract

### Session S16 - Quantum symmetries

Monday, July 19, 16:35 ~ 17:00 UTC-3

## Frobenius-Schur indicators for some families of quadratic fusion categories

### Henry Tucker

#### University of California, Riverside, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakf5d77c2c8741464710d25bf5c60aae5d').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyf5d77c2c8741464710d25bf5c60aae5d = 'ht&#117;ck&#101;r' + '&#64;'; addyf5d77c2c8741464710d25bf5c60aae5d = addyf5d77c2c8741464710d25bf5c60aae5d + '&#117;cr' + '&#46;' + '&#101;d&#117;'; var addy_textf5d77c2c8741464710d25bf5c60aae5d = 'ht&#117;ck&#101;r' + '&#64;' + '&#117;cr' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakf5d77c2c8741464710d25bf5c60aae5d').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyf5d77c2c8741464710d25bf5c60aae5d + '\'>'+addy_textf5d77c2c8741464710d25bf5c60aae5d+'<\/a>';

The family of quadratic fusion categories provides most examples of exotic'' fusion categories, i.e. not coming from finite, Lie, or quantum groups. Recently, Izumi and Grossman families of modular data that are conjectured to give the modular data of Drinfel'd centers of the quadratic fusion categories in general. (In fact, it is true for all known examples.) Using this new modular data, we compute the categorical Frobenius-Schur indicators for these families, an important categorical invariant for fusion categories. Moreover, we look more closely at the relationship between indicators in the fusion category and indicators in its center. This is a preliminary report.