Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras

Abstract

We study quantized Coulomb branches of quiver gauge theories of Jordan type. We prove that the quantized Coulomb branch is isomorphic to the spherical graded Cherednik algebra in the unframed case, and is isomorphic to the spherical cyclotomic rational Cherednik algebra in the framed case. We also prove that the quantized Coulomb branch is a deformation of a subquotient of the Yangian of the affine $\mathfrak{gl}(1)$.

32 pages; v2, 33pages, corrected typos, added acknowledgments

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• Generators for Coulomb branches of quiver gauge theories
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• Gelfand-Tsetlin modules in the Coulomb context
• Twisted holography of defect fusions
• M2-branes and plane partitions
• Abelian mirror symmetry of $\mathcal{N}=(2,2)$ boundary conditions
• Algorithms for representations of quiver Yangian algebras
• Towards the theory of Yangians
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• A domain wall in twisted M-theory
• Integrable systems on multiplicative quiver varieties from cyclic quivers
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• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations
• SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories
• Algebra and geometry of link homology