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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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arxiv 1906.03936 v1 pith:JWTZSX2A submitted 2019-05-24 math.RT math.QA

Nicolas Crampe , Luc Frappat , Luc Vinet This is my paper · ORCID
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keywords algebraquotientbannai-itobrauerrepresentationsuperalgebraactingaction
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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.

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  1. Revisiting the Askey--Wilson algebra with the universal R-matrix of $U_q(sl(2))$

    math.QA 2019-08 conditional novelty 7.0 of 10

    A new R-matrix formula defines the third Askey-Wilson generator as a conjugate of the Casimir element in U_q(sl(2))^{⊗3}, and the Askey-Wilson relations are derived from it.

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