Unipotent elements in small characteristic, IV

TL;DR

This paper studies the structure of nilpotent elements in the dual Lie algebra of reductive groups over algebraically closed fields, proposing a partition into smooth subvarieties and providing explicit results for types A, C, and D.

Contribution

It introduces a new partition of the nilpotent variety in the dual Lie algebra, extending the understanding of unipotent elements in small characteristic.

Findings

Partition of nilpotent variety into smooth subvarieties

Explicit results for types A, C, and D

Connection to unipotent classes over complex numbers

Abstract

We consider the variety of nilpotent elements in the dual of the Lie algebra of a reductive algebraic group over an algebraically closed field. We propose a definition of a partition of this variety into smooth locally closed smooth subvarieties indexed by the unipotent classes in the corresponding group over complex numbers. We obtain explicit results in type A,C and D.