From Twisted Quantum Loop Algebras to Twisted Yangians

TL;DR

This paper demonstrates how twisted Yangians and the Yangian of gl_N can be derived as degenerations of quantum loop algebras and their twisted variants, linking these algebraic structures through a degeneration process.

Contribution

It introduces a method to obtain twisted Yangians and the Yangian of gl_N from quantum loop algebras via degeneration, clarifying their algebraic relationships.

Findings

Twisted Yangians can be derived from quantum loop algebras.

The Yangian of gl_N is obtained through degeneration.

The process connects quantum loop algebras with twisted Yangians.

Abstract

We prove how the Yangian of $\mathfrak{gl}_N$ in its RTT presentation and Olshanski's twisted Yangians for the orthogonal and symplectic Lie algebras can be obtained by a degeneration process from the corresponding quantum loop algebra and some of its twisted analogues.