On a Burnside¹s theorem of spherical fusion categories

 

Siu-Hung (Richard) Ng

Professor, Department of Mathematics, LSU

 

Abstract

A classical theorem of Burnside asserts that a finite group G has no nontrivial self-dual irreducible complex representation if and only if G has odd order.  This result has been recently generalized to integral fusion categories.  However, there exists nontrivial self-dual simple object in a non-integral fusion category of odd dimension.  In this talk, we will discuss a  relation  satisfied  by  the  self-dual  simple objects of  a  modular  tensor  category  of  odd  dimension  in  terms of  their Frobenius-Schur indicators.