The PBW theorem for the affine Yangians
Representation Theory
2018-04-13 v1 Quantum Algebra
Abstract
We prove that the Yangian associated to an untwisted symmetric affine Kac-Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed by the authors in arXiv:1407.7994 as an algebraic formalism of the cohomological Hall algebras. As a consequence, we obtain the Poincare-Birkhoff-Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay-Regelskis-Wendlandt.
Cite
@article{arxiv.1804.04375,
title = {The PBW theorem for the affine Yangians},
author = {Yaping Yang and Gufang Zhao},
journal= {arXiv preprint arXiv:1804.04375},
year = {2018}
}
Comments
12 pages, preliminary version, comments welcome