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