Centralizers of the superalgebra osp(1|2) : the Brauer algebra as a quotient of the Bannai–Ito algebra

Nicolas Crampé (1, 2) , Luc Frappat (3) , Luc Vinet (2)

1 IDP - Institut Denis Poisson
2 CRM - Centre de Recherches Mathématiques [Montréal]
3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

We provide an explicit isomorphism between a quotient of the Bannai-Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra osp(1|2) on the threefold tensor product of its fundamental representation. Finally, a conjecture is proposed to describe the centralizer of osp(1|2) acting on three copies of an arbitrary finite irreducible representation in terms of a quotient of the Bannai-Ito algebra. To the fond memory of Peter Freund, a much esteemed scientist who always generously shared his immense culture.

Domaines: Théorie des représentations [math.RT]; Algèbres quantiques [math.QA]

Nicolas Crampé, Luc Frappat, Luc Vinet. Centralizers of the superalgebra osp(1|2) : the Brauer algebra as a quotient of the Bannai–Ito algebra. Journal of Physics A: Mathematical and Theoretical, 2019, 52 (42), pp.424001. ⟨10.1088/1751-8121/ab433f⟩. ⟨hal-02305470⟩