Rational representations of the Yangian Y(gl_n)

TL;DR

This paper constructs rational representations of the Yangian Y(gl_n), provides explicit formulas for intertwining operators, and conjectures a classification of all finite-dimensional irreducible modules as their images.

Contribution

It introduces a new family of rational representations of Y(gl_n) and explicitly describes the intertwining operators, proposing a conjecture on their completeness for classifying modules.

Findings

Explicit formulas for intertwining operators

Construction of rational representations of Y(gl_n)

Conjecture on classification of irreducible modules

Abstract

We construct a series of rational representations of Y(gl_n) and intertwining operators between them. We find explicit expressions for the images of highest-weight vectors under the intertwining operators. Finally, we state a conjecture that all irreducible finite-dimensional rational Y(gl_n)-modules arise as images of the constructed intertwining operators.