Gauss Coordinates vs Currents for the Yangian Doubles of the Classical Types

TL;DR

This paper explores the relationship between Gauss coordinates and current generators in Yangian doubles of classical types, aiding the development of quantum integrable models and Bethe vector construction.

Contribution

It establishes new relations between Gauss coordinates and current generators for Yangian doubles of types A, B, C, D, enhancing understanding of their algebraic structures.

Findings

Derived explicit relations between Gauss coordinates and currents.

Facilitated construction of Bethe vectors in integrable models.

Improved algebraic understanding of Yangian doubles.

Abstract

We consider relations between Gauss coordinates of $T$-operators for the Yangian doubles of the classical types corresponding to the algebras $\mathfrak{g}$ of $A$, $B$, $C$ and $D$ series and the current generators of these algebras. These relations are important for the applications in the quantum integrable models related to $\mathfrak{g}$-invariant $R$-matrices and construction of the Bethe vectors in these models.