Conjugation properties of tensor product and fusion coefficients. (English) Zbl 1364.81148
Summary: We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them involving hitherto unnoticed observations on ordinary representation theory of finite simple groups of Lie type.
MSC:
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 46M05 | Tensor products in functional analysis |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 20C33 | Representations of finite groups of Lie type |
| 18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
Keywords:
Lie groups; Lie algebras; fusion categories; conformal field theories; quantum symmetries; Drinfeld doublesSoftware:
MagmaReferences:
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