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arXiv · 1605.01314

Classical limits of quantum toroidal and affine Yangian algebras

Alexander Tsymbaliuk
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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.

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Alexander Tsymbaliuk. 2016-05-04. Classical limits of quantum toroidal and affine Yangian algebras. https://doi.org/10.1016/j.jpaa.2017.02.004

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