A note on the O_q(sl₂) algebra

2010/12/23 by Baseilhac, P., Belliard, S.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1012.5261

Abstract

An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian algebra generating O_q(sl₂) currents and the standard generators of the q-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 q-Onsager spectrum generating algebra, the infinite q-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 q-orthogonal polynomials are proposed.

Related

• The higher order q-Dolan-Grady relations and quantum integrable\n systems
• The Lusztig automorphism of the q-Onsager algebra
• Using the quantum torus to investigate the q-Onsager algebra
• The compact presentation for the alternating central extension of the q-Onsager algebra
• The q-Onsager Algebra and the Quantum Torus