The CoHA affine Yangian identification for cyclic quivers

From papers

Let K>2K>2, and let YKY^{K} be the C[Chbar1,Chbar2]C[Chbar_1,Chbar_2]-linear algebra obtained by gluing the two copies of the double deformed current algebra AKA^K constructed from observables on M2 branes. Let Y1,2(K),CoHA\mathcal{Y}^{(K),\operatorname{CoHA}}_{\hbar_1,\hbar_2} denote the CoHA integral form of the affine Yangian associated with gl(K)\mathfrak{gl}(K). The CoHA affine Yangian identification. For any K>2K>2, there is an isomorphism of algebras

YKY1,2(K),CoHA.Y^{K} \simeq \mathcal{Y}^{(K),\operatorname{CoHA}}_{\hbar_1,\hbar_2}.

This is an expected identification between the algebra constructed in the physics literature and the CoHA integral form of the affine Yangian; the supplied source does not give evidence that it has been proved or disproved.

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Sources & referencesView supporting material

Primary source

Shivang Jindal, “CoHA of Cyclic Quivers and an Integral Form of Affine Yangians”, arXiv:2408.02618 (2026).

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