The Hesselink stratification of nullcones and base change

Details The Hesselink stratification of nullcones and base change The Hesselink stratification of nullcones and base change

2011-08-30

arxiv.org/abs/1108.5889v2

Mathematics

Representation Theory

30 pages

Scientific paper

Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic $p \ge 0$. We give a case-free proof of Lusztig's conjectures [Unipotent elements in small characteristic, {\em Transform. Groups} 10 (2005), 449--487] 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 $\gl$ and the coadjoint action of $G$ on $\gl^*$.

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