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

Nicolas Crampé; Luc Frappat; Luc Vinet

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, *}

* Corresponding author

1 IDP - Institut Denis Poisson

2 CRM - Centre de Recherches Mathématiques [Montréal]

3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

Abstract : 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.

Document type :

Journal articles

Domain :

Mathematics [math] / Representation Theory [math.RT]

Mathematics [math] / Quantum Algebra [math.QA]

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https://hal-univ-tours.archives-ouvertes.fr/hal-02305470
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Submitted on : Friday, October 4, 2019 - 11:18:23 AM
Last modification on : Monday, October 28, 2019 - 10:32:28 AM

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

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