An imaginary PBW basis for quantum affine algebras of type 1

TL;DR

This paper constructs a PBW basis for quantum affine algebras of type 1, focusing on the imaginary positive root system, advancing the understanding of their algebraic structure.

Contribution

It introduces an imaginary PBW basis for quantum affine algebras of type 1, a novel approach in the context of their root systems.

Findings

Established a PBW basis related to the imaginary positive roots

Provided explicit construction methods for the basis

Enhanced the algebraic understanding of quantum affine algebras

Abstract

Let $\hat{\mathfrak g}$ be an affine Lie algebra of type 1. We give a PBW basis for the quantum affine algebra $U_q(\hat{\mathfrak g})$ with respect to the triangular decomposition of $\hat{\mathfrak g}$ associated with the imaginary positive root system.