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The coordinate ring of the universal centralizer via Demazure operators
Tom Gannon, Victor Ginzburg
We give a simple description of the coordinate ring of the universal centralizer associated to a simply connected semisimple group. To this end, we prove a general result on Weil r…
Quantization of the universal centralizer and central D-modules
Tom Gannon, Victor Ginzburg
The group scheme of universal centralizers of a complex reductive group has a quantization called the spherical nil-DAHA. The category of modules over this ring is equivalent,…
The cotangent bundle of and Kostant-Whittaker descent
Tom Gannon
We prove that the algebra of functions on the cotangent bundle of the parabolic base affine space for a reductive group and a parabolic subgroup is isomorphic…
Differential operators on the base affine space of and quantized Coulomb branches
Tom Gannon, Harold Williams
We show that the algebra of differential operators on the base affine space of is the quantized Coulomb branch of a certain 3d quiver gau…
The universal category and the Gelfand-Graev action
Tom Gannon
We show that the definition and many useful properties of Soergel's functor extend to "universal" variants of the BGG category , such as the category whic…