  In this paper we show that integral fusion categories with rational structure
constants admit a natural group of symmetries given by the Galois group of
their character tables. We also generalize a well known result of Burnside from
representation theory of finite groups. More precisely, we show that any row
corresponding to a non invertible object in the character table of a weakly
integral fusion category contains a zero entry.

Quantum Algebra;Category Theory;Representation Theory