On Harada's identity and some other consequences of Burnside's vanishing property

Autor: Burciu, S.
Rok vydání: 2023
Předmět:
Druh dokumentu: Working Paper
Popis: In this short note, we prove some consequences of Burnside's vanishing property \cite{b-pa}. It is known that Harada's identity concerning the product of all conjugacy classes 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. In the second part, we prove some structural results concerning nilpotent and modular fusion categories. As an application we show that any fusion category of dimension $p^2q^2r^2d$ with $pComment: 8 pages. Comments are welcome!
Databáze: arXiv