Coproduct for the Yangian of an affine Kac-Moody algebra

Curtis Wendlandt; Hiraku Nakajima; Nicolas Guay

Coproduct for the Yangian of an affine Kac-Moody algebra

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arxiv 1701.05288 v3 pith:MH4XA5TC submitted 2017-01-19 math.QA math.RT

Coproduct for the Yangian of an affine Kac-Moody algebra

Nicolas Guay , Hiraku Nakajima , Curtis Wendlandt This is my paper

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keywords algebracoproductkac-moodyyangianaffineassociatedconstructexplain

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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.

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Weyl group reflections act as Seiberg-like dualities on A_n quiver gauge theories, mapping stability chambers to each other while conjecturally leaving the quiver Yangian Y(sl_{n+1}) invariant.