String Math Seminar: Harold Williams (USC) ” Differential operators on the base affine space and quantized Coulomb branches “

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Abstract: We discuss joint work with Tom Gannon, showing that the algebra $D(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is the quantized Coulomb branch of a certain 3d $\mathcal{N} = 4$ quiver gauge theory. In the semiclassical limit this confirms a conjecture of Dancer-Hanany-Kirwan on the universal hyperk\”ahler implosion of $SL_n$. In fact, we prove a generalization interpreting an arbitrary unipotent reduction of $T^* SL_n$ as a Coulomb branch. These results also provide a new interpretation of the Gelfand-Graev Weyl group symmetry of $D(SL_n/U)$.