Coproduct for the Yangian of an affine Kac-Moody algebra

Abstract

Given an affine Kac-Moody algebra, we explain how to construct a coproduct for its associated Yangian. In order to prove that this coproduct is an algebra homomorphism, we obtain, in the first half of this paper, a minimalistic presentation of the Yangian when the Kac-Moody algebra is, more generally, symmetrizable.

arXiv comment38 pages

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• Rational Lax matrices from antidominantly shifted extended Yangians: BCD types
• Braid Group Action on Affine Yangian
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• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
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• Vertex Representations for Yangians of Kac-Moody algebras
• More on Affine Dynkin Quiver Yangians
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• Towards the theory of Yangians
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• Quantum N-toroidal algebras and extended quantized GIM algebras of N-fold affinization
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products
• Braid group actions, Baxter polynomials, and affine quantum groups
• An Overview of Crystals and Double Quiver Yangians
• Theta series for quantum loop algebras and Yangians
• Orthosymplectic Yangians
• The restricted quantum double of the Yangian
• On a conjecture of Khoroshkin and Tolstoy
• The PBW theorem for the affine Yangians
• Weyl Mutations in Quiver Yangians
• Twisted Affine Yangian and Rectangular $W$-algebra of type $D$
• Yangians vs minimal W-algebras: a surprizing coincidence