Limits of quantum toroidal and affine Yangian
In this short note, we compute the classical limits of the quantum toroidal and the affine Yangian algebras of sl(n) by generalizing our arguments for the case of gl(1) from arXiv:1404.5240. These results were mentioned as motivation in the recent study of toroidal algebras by [Feigin-Jimbo-Miwa-Mukhin], while they played a crucial role in the recent paper of the author and Bershtein. An alternative proof of our key isomorphisms for n>2 was first established by [Varagnolo-Vasserot]. We also discuss some consequences of these results.