Two-parameter quantum ane algebra — 1 articles found.

Fermionic Realization of Two-Parameter Quantum Affine Algebra $U_{r;s}(C_l^{(1)})$

C. R. Math. Rep. Acad. Sci. Canada Vol. 38 (1) 2016, pp. 1-15
Vol.38 (1) 2016
Naihuan Jing; Honglian Zhang Details
(Received: 2014-11-08 , Revised: 2015-02-27 )
(Received: 2014-11-08 , Revised: 2015-02-27 )

Naihuan Jing,School of Mathematical Sciences, South China University of Technology, Guangzhou 510640,
China and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA; e-mail: jing@math.ncsu.edu

Honglian Zhang,Department of Mathematics, Shanghai University, Shanghai 200444, China; e-mail: hlzhangmath@shu.edu.cn

Abstract/Résumé:

We construct a Fock space representation and the action of the two-parameter quantum algebra \(U_{r,s}(\frak{gl}_{\infty})\) using extended Young diagrams. In particular, we obtain an integrable representation of the two-parameter quantum affine algebra of type \(C_n^{(1)}\) which is a two-parameter generalization of Kang-Misra-Miwa’s realization.

Nous construisons une représentation sur un espace de Fock de l’algèbre quantique à deux paramètres \(U_{r,s}(\frak{gl}_{\infty})\) en utilisant les diagrammes de Young prolongés. En particulier, on obtient une représentation intégrable de l’algèbre quantique affine à deux paramètres de type \(C_n^{(1)}\) qui est une généralization à deux paramètres de la réalization de Kang-Misra-Miwa.

Keywords: Fock space, Two-parameter quantum ane algebra, Young diagram, fermionic realization

AMS Subject Classification: Quantum groups (quantized enveloping algebras) and related deformations 17B37

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