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 $U_q({\mathfrak{sl}}_2)$ 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.

arXiv comment23 pages, 5 figures

References in corpus (7)

• Superintegrability in two dimensions and the Racah-Wilson algebra
• The Askey-Wilson algebra and its avatars
• The higher rank $q$-deformed Bannai-Ito and Askey-Wilson algebra
• Revisiting the Askey--Wilson algebra with the universal R-matrix of $U_q(sl(2))$
• Centralizers of the superalgebra osp(1|2): the Brauer algebra as a quotient of the Bannai-Ito algebra
• Temperley-Lieb, Birman-Murakami-Wenzl and Askey-Wilson algebras and other centralizers of $U_q({\mathfrak{sl}}_2)$
• Bannai-Ito algebras and the universal R-matrix of osp(1|2)

Cited by in corpus (2)

• Spin models and distance-regular graphs of $q$-Racah type
• Uncoiled affine Temperley-Lieb algebras and their Wenzl-Jones projectors