The coordinate ring of the universal centralizer via Demazure operators

Associated to a complex reductive group G is a variety originally considered by Lusztig known as the group scheme of universal centralizers. Our main result describes this variety as an affine blow up of the quotient of the cotangent bundle of a maximal torus of G by its action of the Weyl group. After making this result more precise and comparing it to previous results in the literature, we will introduce the notion of the invariant Weil restriction (also known as the transverse Hilbert scheme) and explain how our results generalize to this setting. This is joint with Victor Ginzburg.

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