Yangians and Baxter's relations

TL;DR

This paper explores the representation theory of Yangians associated with simple Lie algebras, establishing Baxter's TQ relations for asymptotic modules and connecting to Hernandez--Jimbo's limit construction.

Contribution

It introduces asymptotic modules as analytic continuations of Kirillov--Reshetikhin modules and proves Baxter's relations in this context, extending the understanding of Yangian representations.

Findings

Established Baxter's TQ relations for asymptotic modules

Constructed asymptotic modules via analytic continuation

Connected Yangian modules to shifted Yangians through Hernandez--Jimbo's limit

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.