More on Affine Dynkin Quiver Yangians

Abstract

We consider the quiver Yangians associated to general affine Dynkin diagrams. Although the quivers are generically not toric, the algebras have some similar structures. The odd reflections of the affine Dynkin diagrams should correspond to Seiberg duality of the quivers, and we investigate the relations of the dual quiver Yangians. We also mention the construction of the twisted quiver Yangians. It is conjectured that the truncations of the (twisted) quiver Yangians can give rise to certain $\mathcal{W}$-algebras. Incidentally, we give the screening currents of the $\mathcal{W}$-algebras in terms of the free field realization in the case of generalized conifolds. Moreover, we discuss the toroidal and elliptic algebras for any general quivers.

arXiv comment61 pages; v3: minor corrections

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• Quantum toroidal algebras and solvable structures in gauge/string theory
• Algorithms for representations of quiver Yangian algebras
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• An Overview of Crystals and Double Quiver Yangians
• Weyl Mutations in Quiver Yangians
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations