Yangians and Baxter's relations
Quantum Algebra
2020-07-29 v4 Mathematical Physics
math.MP
Representation Theory
Abstract
We study a category O of representations of the Yangian associated to an arbitrary finite-dimensional complex simple Lie algebra. We obtain asymptotic modules as analytic continuation of a family of finite-dimensional modules, the Kirillov--Reshetikhin modules. In the Grothendieck ring we establish the three-term Baxter's TQ relations for the asymptotic modules. We indicate that Hernandez--Jimbo's limit construction can also be applied, resulting in modules over anti-dominantly shifted Yangians.
Keywords
Cite
@article{arxiv.1808.02294,
title = {Yangians and Baxter's relations},
author = {Huafeng Zhang},
journal= {arXiv preprint arXiv:1808.02294},
year = {2020}
}
Comments
v1: 18 pages. v2: some inaccuracy in Table (14) and at the first step of the proof of Theorem 20 corrected, references updated. v3: 20 pages, a new section on prefundamental modules added. v4: published version