Yangian doubles of classical types and their vertex representations

Abstract

The Yangian double ${\text{DY}}_{\hslash }({\mathfrak{g}}_N)$ 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 ${\text{DY}}_{\hslash }({\mathfrak{g}}_N)$ of non-simply-laced types are explicitly constructed.

50 pages, 0 figures. Revised version