The Hesselink stratification of nullcones and base change

Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p≥0. We give a case-free proof of Lusztig's conjectures (Lusztig in Transform. Groups 10:449-487, 2005) on so-called unipotent pieces. This presents a uniform picture of the unipotent elements of G which can be viewed as an extension of the Dynkin-Kostant theory, but is valid without restriction on p. We also obtain analogous results for the adjoint action of G on its Lie algebra g and the coadjoint action of G on g*. © 2012 Springer-Verlag.