Burnside vanishing type properties for fusion categories

Abstract: A classical result of Burnside in the character theory of finite groups states that any irreducible non-linear character of a finite group vanishes on at least one element of the group. In this talk, we show that a similar vanishing property holds for weakly integral fusion categories. It is known that Harada’s identity, related with the product of all conjugacy class sums of a finite group, is a consequence of Burnside’s vanishing property of characters. We prove a similar formula for any weakly integral fusion category and discuss some other new consequences of this result. This is partially joint work with S. Palcoux.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home