Differential Operators on the Base Affine Space of SLn and Quantized Coulomb Branches

We show that the algebra D_ (SLₙ/U) of differential operators on the base affine space of SLₙ is the quantized Coulomb branch of a certain 3d N = 4 quiver gauge theory. In the semiclassical limit this proves a conjecture of Dancer–Hanany–Kirwan about the universal hyperkähler implosion of SLₙ. We also formulate and prove a generalization identifying the Hamiltonian reduction T* SLₙ\ /\!/ ψ U as a Coulomb branch for an arbitrary unipotent character ψ. As an application of our results, we provide a new interpretation of the Gelfand–Graev symmetric group action on D_ (SLₙ/U).