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

TL;DR

This paper constructs fundamental modules for the two-parameter quantum affine algebra of type A using Young diagrams and provides a fermionic realization of the algebra, advancing the understanding of its structure.

Contribution

It introduces a fermionic realization of the two-parameter quantum affine algebra and constructs all fundamental modules via a combinatorial Young diagram model.

Findings

Fermionic realization of $U_{r,s}(sl_n)$ achieved.

All fundamental modules explicitly constructed.

Provides combinatorial model for the algebra's modules.

Abstract

We construct all fundamental modules for the two parameter quantum affine algebra of type $A$ using a combinatorial model of Young diagrams. In particular we also give a fermionic realization of the two-parameter quantum affine algebra.