Yangians and Baxter's relations

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.

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