Coulomb branches of quiver gauge theories with symmetrizers

Abstract

We generalize the mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ SUSY quiver gauge theories due to Nakajima (2016) and Braverman et al. (2018, 2019) to the cases with symmetrizers. We obtain generalized affine Grassmannian slices of type $BCFG$ as examples of the construction, and their deformation quantizations via truncated shifted Yangians. Finally, we study modules over these quantizations and relate them to the lower triangular part of the quantized enveloping algebra of type $ADE$.