English

Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra

Quantum Algebra 2019-12-20 v2 Mathematical Physics math.MP

Abstract

The higher rank Askey-Wilson algebra was recently constructed in the nn-fold tensor product of Uq(sl2)U_q(\mathfrak{sl}_2). In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank one Askey-Wilson algebra. We extend the known construction algorithm by several equivalent methods, using a novel coaction. These allow to simplify calculations significantly. At the same time, this provides a proof of the corresponding relations for the higher rank qq-Bannai-Ito algebra.

Keywords

Cite

@article{arxiv.1908.11654,
  title  = {Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra},
  author = {Hadewijch De Clercq},
  journal= {arXiv preprint arXiv:1908.11654},
  year   = {2019}
}