Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 120, 23 pages      arXiv:2006.01579      https://doi.org/10.3842/SIGMA.2020.120

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

Andrii Liashyk ^a and Stanislav Z. Pakuliak ^b
a) Skolkovo Institute of Science and Technology, Moscow, Russia
^b) Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Str., Moscow, 119991, Russia

Received June 03, 2020, in final form November 15, 2020; Published online November 22, 2020

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.

Key words: Yangians; Gauss decomposition; Drinfeld currents.

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