On Grothedieck rings of rank $4$ self-dual fusion categories

Abstract

Let $\C$ be a self-dual fusion category of rank $4$ which has a nontrivial proper fusion subcategory. We identify three new families of Grothendieck rings for $\C$: one of them is completely determined, the other two are parameterized by several non-negative integers.

This paper has not been submitted to any journal. If someone can reduce the number of parameters, please contact me. Any cooperation, improvement and comments are very welcome