English

Classical limits of quantum toroidal and affine Yangian algebras

Representation Theory 2019-02-12 v2

Abstract

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 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 arXiv:1512.09109 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.

Keywords

Cite

@article{arxiv.1605.01314,
  title  = {Classical limits of quantum toroidal and affine Yangian algebras},
  author = {Alexander Tsymbaliuk},
  journal= {arXiv preprint arXiv:1605.01314},
  year   = {2019}
}

Comments

v1: 10 pages; v2: 12 pages, minor corrections, some details added