The paper proposes that twisted-sector local operators transform in *-representations of the tube algebra of a higher fusion category symmetry, and classifies these representations using higher S-matrices.
Representation and character theory in 2-categories
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abstract
We define the character of a group representation in a 2-category C. For linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory defined on pairs of commuting elements of the group. We discuss some examples and prove a formula for the character of the induced representation.
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Unitary Categorical Symmetries
The paper proposes that twisted-sector local operators transform in *-representations of the tube algebra of a higher fusion category symmetry, and classifies these representations using higher S-matrices.