Fermionic realization of two-parameter quantum affine algebra $U_{r,s}(C_l^{(1)})$

TL;DR

This paper constructs a Fock space representation of a two-parameter quantum affine algebra of type C, extending previous realizations and providing new integrable representations using extended Young diagrams.

Contribution

It introduces a novel Fock space construction for the two-parameter quantum affine algebra of type C, generalizing existing one-parameter models.

Findings

Established a Fock space representation using extended Young diagrams.

Derived an integrable representation of $U_{r,s}(C_n^{(1)})$.

Generalized Kang-Misra-Miwa's realization to two parameters.

Abstract

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.