The wonderful compactication and the universal centralizer

Let Gbe a complex semisimple algebraic group of adjoint type and \overline{G} the wonderful compacti

cation. We show that the closure in \overline{G} of the centralizer G^eof a regular nilpotent e \in Lie(G)is isomorphic to the Peterson variety. We generalize this result to show that for any regular x \in Lie(G), the closure of the centralizer G^xin \overline{G}is isomorphic to the closure of a general G^x-orbit in the flag variety. We consider the family of all such centralizer closures, which is a partial compactication of the universal centralizer. We show that it has a natural log-symplectic Poisson structure that extends the usual symplectic structure on the universal centralizer.

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Monday, February 26, 2018 - 14:00 to 15:30
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