Irreducibility criterion for tensor products of Yangian evaluation modules

Abstract

The evaluation homomorphisms from the Yangian ${\rm Y}(\mathfrak {gl}\sb n)$ to the universal enveloping algebra ${\rm U}(\mathfrak {gl}\sb n)$ allow one to regard the irreducible finite-dimensional representations of $\mathfrak {gl}\sb n$ as Yangian modules. We give necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules.