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.

arXiv commentv1: 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

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• A Shortcut to the Q-Operator
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• Finite type modules and Bethe ansatz equations
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Cited by in corpus (4)

• Poles of finite-dimensional representations of Yangians
• A functor for constructing $R$-matrices in the category $\mathcal{O}$ of Borel quantum loop algebras
• Theta series for quantum loop algebras and Yangians
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$