Quiver Yangians and -algebras for generalized conifolds

Abstract

Abstract We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach by Guay–Nakajima–Wendlandt. We also prove that the quiver Yangians related by Seiberg duality are indeed isomorphic. Then we discuss their connections to -algebras analogous to the study by Ueda. In particular, the universal enveloping algebras of the -algebras are truncations of the quiver Yangians, and therefore they naturally have truncated crystals as their representations.