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

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.
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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, IOP Publishing, 2019, 52 (42), pp.424001. ⟨10.1088/1751-8121/ab433f⟩. ⟨hal-02305470⟩

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