Wedge modules for two-parameter quantum groups

TL;DR

This paper computes the Yang-Baxterization R(z) for two-parameter quantum affine algebra of type A and constructs fundamental representations as wedge products using fusion, advancing the understanding of quantum group representations.

Contribution

It introduces a method to explicitly construct fundamental representations of two-parameter quantum affine algebras via wedge products, utilizing the fusion procedure.

Findings

Computed Yang-Baxterization R(z) for the algebra

Constructed fundamental representations as wedge products

Enhanced understanding of quantum group representations

Abstract

The Yang-Baxterization R(z) of the trigonometric R-matrix is computed for the two-parameter quantum affine algebra of type A. Using the fusion procedure we construct all fundamental representations of the quantum algebra as wedge products of the natural representation.