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Journal Articles Annales Henri Poincaré Year : 2023

Askey–Wilson Braid Algebra and Centralizer of $U_q(\mathfrak {sl}_2)$

Abstract

A presentation of the centralizer of the three-fold tensor product of the spin s representation of the quantum group Uq(sl2) is provided. It is expressed as a quotient of the Askey-Wilson braid algebra. This newly defined algebra combines the Askey-Wilson relations with the braid group relations, on three strands, together with a characteristic equation of degree 2s+1 for the braid generators. Explicit bases are given for the centralizer.

Dates and versions

hal-04027988 , version 1 (14-03-2023)

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Nicolas Crampé, Loïc Poulain D’andecy, Luc Vinet, Meri Zaimi. Askey–Wilson Braid Algebra and Centralizer of $U_q(\mathfrak {sl}_2)$. Annales Henri Poincaré, 2023, ⟨10.1007/s00023-023-01275-4⟩. ⟨hal-04027988⟩
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