Abstract

Let G be a semisimple complex algebraic group of adjoint type. We consider a multiplicative analogue of the universal centralizer of G --- a family of centralizers parametrized by the regular conjugacy classes of the simply-connected cover of G. This multiplicative analogue has a natural symplectic structure and sits as a transversal in a variation of the quasi-Poisson double D(G). We show that D(G) extends to a smooth groupoid over the wonderful compactification of G, and we use this to construct a partial compactification of the multiplicative universal centralizer.