Intertwiners of Yangian representations

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.