Yangians and Baxter's relations

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.

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