On Guay's evaluation map for affine Yangians
Representation Theory
2020-12-08 v2 Quantum Algebra
Abstract
We give a detailed proof of the existence of evaluation map for affine Yangians of type A to clarify that it needs an assumption on parameters. This map was first found by Guay but a proof of its well-definedness and the assumption have not been written down in the literature. We also determine the highest weights of evaluation modules defined as the pull-back of integrable highest weight modules of the affine Lie algebra by the evaluation map.
Keywords
Cite
@article{arxiv.1806.09884,
title = {On Guay's evaluation map for affine Yangians},
author = {Ryosuke Kodera},
journal= {arXiv preprint arXiv:1806.09884},
year = {2020}
}
Comments
18 pages; v2, 21 pages, corrected the definition of affine \mathfrak{gl}_N in Section 2.2 and the proof of Lemma 3.3. The correction is available on 10.1007/s10468-020-10011-z