English

A note on the $O_q(\hat{sl_2})$ algebra

Mathematical Physics 2010-12-24 v1 math.MP

Abstract

An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian algebra generating Oq(sl2^)O_q(\hat{sl_2}) currents and the standard generators of the qq-Onsager algebra is proposed. Two straightforward applications of the result are then considered: First, for the class of quantum integrable models which integrability condition originates in the qq-Onsager spectrum generating algebra, the infinite qq-deformed Dolan-Grady hierarchy is derived - bypassing the transfer matrix formalism. Secondly, higher Askey-Wilson relations that arise in the study of symmetric special functions generalizing the Askey-Wilson qq-orthogonal polynomials are proposed.

Keywords

Cite

@article{arxiv.1012.5261,
  title  = {A note on the $O_q(\hat{sl_2})$ algebra},
  author = {P. Baseilhac and S. Belliard},
  journal= {arXiv preprint arXiv:1012.5261},
  year   = {2010}
}

Comments

11 pages

R2 v1 2026-06-21T17:03:42.646Z