Yangian doubles of classical types and their vertex representations

TL;DR

This paper introduces Yangian doubles for classical Lie algebra types, provides their Drinfeld presentation via Gauss decomposition, and constructs explicit bosonization level 1 realizations for non-simply-laced types.

Contribution

It extends the theory of Yangian doubles to classical types and offers explicit bosonization constructions for non-simply-laced cases.

Findings

Yangian doubles for classical types are formally introduced.

Drinfeld presentation obtained through Gauss decomposition.

Explicit bosonization realizations at level 1 are constructed.

Abstract

The Yangian double $\text{DY}_{\hbar}(\mathfrak{g}_N)$ is introduced for the classical types of $\mathfrak{g}_N=\mathfrak{o}_{2n+1}$, $\mathfrak{sp}_{2n}$, $\mathfrak{o}_{2n}$. Via the Gauss decomposition of the generator matrix, the Yangian double is given the Drinfeld presentation. In addition, bosonization of level $1$ realizations for the Yangian double $\text{DY}_{\hbar}(\mathfrak{g}_N)$ of non-simply-laced types are explicitly constructed.