Degeneration of trigonometric dynamical difference equations for quantum loop algebras to trigonometric Casimir equations for Yangians

TL;DR

This paper demonstrates how certain difference equations in quantum affine algebras simplify to differential equations in Yangians through a specific degeneration process, revealing a deep connection between these algebraic structures.

Contribution

It establishes a precise degeneration from trigonometric dynamical difference equations to Casimir differential equations, clarifying the relationship between quantum loop algebras and Yangians.

Findings

Difference equations degenerate to differential equations

Connection between quantum loop algebras and Yangians clarified

Provides a new perspective on algebraic degeneration processes

Abstract

We show that, under Drinfeld's degeneration of quantum loop algebras to Yangians, the trigonometric dynamical difference equations for the quantum affine algebra degenerate to the trigonometric Casimir differential equations for Yangians.