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We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are2d TQFTs whose fusion rules can be diagonalized. We show that, in this specialbasis, the 0-form symmetries always act as permutations while 1-form symmetriesact by phases. This leads to an explicit description of the gauging of thesesymmetries. One application of our results is a generalization of theequivariant Verlinde formula to the case of general Lie groups. The generalizedformula leads to many predictions for the geometry of Hitchin moduli spaces,which we explicitly check in several cases with low genus and SO(3) gaugegroup.

Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups