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

Abstract

We consider relations between Gauss coordinates of 𝑇-operators for the Yangian doubles of the classical types corresponding to the algebras 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 𝖌-invariant 𝑅-matrices and the construction of the Bethe vectors in these models.