We study a category $${\mathcal {O}}$$ 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.

中文翻译：

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Yangians 和 Baxter 的关系

我们研究了与任意有限维复数简单李代数相关联的 Yangian 表示的类别 $${\mathcal {O}}$O。我们获得渐近模块作为有限维模块族 Kirillov-Reshetikhin 模块的解析延续。在 Grothendieck 环中，我们为渐近模建立三项 Baxter 的 TQ 关系。我们指出 Hernandez-Jimbo 的极限构造也可以应用，导致模块超过反显性偏移的 Yangians。