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

Abstract : An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian algebra generating $O_q(\hat{sl_2})$ 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00784873
Contributor : Pascal Baseilhac <>
Submitted on : Monday, February 4, 2013 - 6:16:24 PM
Last modification on : Tuesday, November 5, 2019 - 5:14:34 PM

### Identifiers

• HAL Id : hal-00784873, version 1
• ARXIV : 1012.5261

### Citation

P. Baseilhac, S. Belliard. A note on the $O_q(\hat{sl_2})$ algebra. 2010. ⟨hal-00784873⟩

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