Intertwiners of Yangian representations

TL;DR

This paper constructs and analyzes intertwiners for type gℓ(n) Yangian algebra representations, revealing how parameter permutations influence representation types and providing explicit formulas based on R-matrix relations.

Contribution

It explicitly constructs intertwiners for Yangian representations depending on parameters, showing their relation to permutations and R-matrix structures.

Findings

Intertwiners exist when parameters are permuted.

Intertwiners are products of elementary permutation operators.

Parameter dependence distinguishes representation types.

Abstract

We construct type $g\ell(n)$ Yangian algebra evaluations of order $N$ embedded in Heisenberg algebras and consider their representations having a highest weight. These Yangian algebra presentations depend on $nN$ parameters. We construct explicitly intertwiners, which exist if the parameter arrays are related by permutations. The intertwiners are products of elementary adjacent parameter permutation operators derived from $R$ operators obeying Yang-Baxter relations. Permutation coefficients appear in the action on representations. Their dependence on the parameters allows to distinguish the types of representations.