Conjugation Properties of Tensor Product and Fusion Coefficients

Robert Coquereaux (1, 2) , Jean-Bernard Zuber (3)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332
3 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Mots clés: Lie algebras; Lie groups; fusion categories; conformal field theories; Drinfeld doubles; quantum symmetries

Domaines: Physique mathématique [math-ph]; Algèbres quantiques [math.QA]; Théorie des représentations [math.RT]; Physique des Hautes Energies - Théorie [hep-th]

Robert Coquereaux, Jean-Bernard Zuber. Conjugation Properties of Tensor Product and Fusion Coefficients. Letters in Mathematical Physics, 2017, 107 (2), pp.291-299. ⟨10.1007/s11005-016-0901-3⟩. ⟨hal-01335622⟩