61 research outputs found
On Harada's identity and some other consequences of Burnside's vanishing property
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 with prime
numbers and a square-free integer is weakly-group theoretical.Comment: 8 pages. Comments are welcome
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