On finite-dimensional representations of two-parameter quantum affine algebras

TL;DR

This paper introduces Drinfeld polynomials for modules of two-parameter quantum affine algebras and characterizes finite-dimensional representations through specific polynomial conditions.

Contribution

It defines Drinfeld polynomials in the two-parameter setting and provides a characterization of finite-dimensional modules based on these polynomials.

Findings

Finite-dimensional modules are characterized by sets of Drinfeld polynomial pairs.

A new notion of Drinfeld polynomials is introduced for two-parameter quantum affine algebras.

The paper establishes conditions for modules to be finite-dimensional.

Abstract

A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.