Yangian doubles of classical types and their vertex representations

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.