Fusion rules for Z/2Z permutation gauging

Abstract

In this note, we examine the gauging of the Z/2Z permutation action on the tensor square of a modular tensor category C. When C is unpointed we provide formulas for the fusion rules of the gauged category, which nontrivially involves the modular data of C. Our technique highlights the use of generalized Frobenius-Schur indicators. We discuss several examples related to quantum groups at roots of unity.