BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar On conjugacy classes and Grothendieck rings of premodular categories
On conjugacy classes and Grothendieck rings of premodular categories
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sébastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
Sebastian Burciu
Time
Wednesday, September 14, 2022 1:30 PM - 3:00 PM
Venue
Online
Online
Zoom 537 192 5549 (BIMSA)
Abstract
Recently, Shimizu introduced the notion of conjugacy classes for fusion categories, extending the classical notion of conjugacy classes for groups. In this talk we present some new properties of conjugacy classes for pivotal fusion categories. In particular we prove a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of a such fusion category. For a braided weakly integral fusion category C we show that these structure constants multiplied by dim(C) are non-negative integers, extending some results ob- tained recently by Zhou and Zhu in the settings of semisimple quasitriangular Hopf algebras. The talk is based on S. Burciu "Structure constants of premodular categories" Bull. Lond. Math. Soc. 53 (2021), no. 3, 777–791 and a work in progress of the author.

References:

https://doi.org/10.1112/blms.12459

https://arxiv.org/abs/2002.05483