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

References in corpus (3)

• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• Equivalences between three presentations of orthogonal and symplectic Yangians
• Vertex Representations for Yangians of Kac-Moody algebras

Cited by in corpus (6)

• The formal shift operator on the Yangian double
• $h$-adic quantum vertex algebras in types $B$, $C$, $D$ and their $\varphi$-coordinated modules
• On the R-matrix realization of quantum loop algebras
• Poles of finite-dimensional representations of Yangians
• Algebraic Bethe ansatz for ${\mathfrak{o}}_{2n+1}$-invariant integrable models
• Center of the Yangian double in type A