Askey-Wilson braid algebra and centralizer of $U_q(\mathfrak{sl}_2)$
Representation Theory
2023-07-13 v1 Mathematical Physics
math.MP
Quantum Algebra
Abstract
A presentation of the centralizer of the three-fold tensor product of the spin representation of the quantum group 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 for the braid generators. Explicit bases are given for the centralizer.
Keywords
Cite
@article{arxiv.2206.11150,
title = {Askey-Wilson braid algebra and centralizer of $U_q(\mathfrak{sl}_2)$},
author = {Nicolas Crampe and Loic Poulain d'Andecy and Luc Vinet and Meri Zaimi},
journal= {arXiv preprint arXiv:2206.11150},
year = {2023}
}
Comments
23 pages, 5 figures