Vertex Representations for Yangians of Kac-Moody algebras

TL;DR

This paper constructs vertex operator-based representations of Yangians associated with simply laced Kac-Moody algebras and proves the PBW property for their affine variants, advancing understanding of their algebraic structure.

Contribution

It introduces a vertex operator approach to represent Yangians of simply laced Kac-Moody algebras and establishes the PBW property for affine Yangians.

Findings

Constructed vertex operator representations for Yangians.

Proved PBW property for simply laced affine Yangians.

Enhanced understanding of algebraic structures of Yangians.

Abstract

Using vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.