Non-Invertible Symmetries and their Representations

In the first half of the talk, I will review the notion of non-invertible symmetries and how they help us to analyze certain strongly coupled QFTs like 2d Adjoint QCD. Then, I discuss the representation theory of non-invertible symmetries and use it to derive selection rules on correlation functions of local operators. Using this understanding, I drive a Cardy-like formula in 2d CFTs with a finite non-invertible symmetry. More precisely, we find the asymptotic density of states transforming under an irreducible representation of a non-invertible symmetry.