The partial compactification of the universal centralizer
By Ana Balibanu
Also appears in collection : Symplectic representation theory / Théorie symplectique des représentations
Let $G$ be a semisimple algebraic group of adjoint type. The universal centralizer is the family of centralizers in $G$ of regular elements in Lie$(G)$, parametrized by their conjugacy classes. It has a natural symplectic structure, obtained by Hamiltonian reduction from the cotangent bundle $T^∗ G$. We consider a partial compactification of the universal centralizer, where each centralizer fiber is replaced by its closure inside the wonderful compactification of $G$. The symplectic structure extends to a log-symplectic Poisson structure on this partial compactification, whose fibers are isomorphic to regular Hessenberg varieties.
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