Projects per year
Abstract
A linear étale representation of a complex algebraic group G is given by a complex algebraic Gmodule V such that G has a Zariskiopen orbit in V and $\dim G=\dim V$ . A current line of research investigates which reductive algebraic groups admit such étale representations, with a focus on understanding common features of étale representations. One source of new examples arises from the classification theory of nilpotent orbits in semisimple Lie algebras. We survey what is known about reductive algebraic groups with étale representations and then discuss two classical constructions for nilpotent orbit classifications due to Vinberg and to Bala and Carter. We determine which reductive groups and étale representations arise in these constructions and we work out in detail the relation between these two constructions.
Original language  English 

Pages (fromto)  113125 
Number of pages  13 
Journal  Bulletin of the Australian Mathematical Society 
Volume  106 
Issue number  1 
DOIs  
Publication status  Published  Aug 2022 
Keywords
 17B10
 20G05
 22E46
 flat Lie groups
 nilpotent orbits
 prehomogeneous vector spaces
 étale representations
Projects
 1 Finished

Computing with Lie groups and algebras: nilpotent orbits and applications
Dietrich, H. & de Graaf, W. A.
1/04/19 → 1/08/23
Project: Research