English

Minuscule weights and Chevalley groups

Representation Theory 2016-09-28 v4

Abstract

The traditional construction of Chevalley groups relies on the choice of certain signs for a Chevalley basis of the underlying Lie algebra~g\mathfrak{g}. Recently, Lusztig simplified this construction for groups of adjoint type by using the "canonical basis" of the adjoint representation of~g\mathfrak{g}, in particular, no choices of signs are required. The purpose of this note is to extend this to Chevalley groups which are not necessarily of adjoint type, using Jantzen's explicit models of the minuscule highest weight representations of~g\mathfrak{g}.

Cite

@article{arxiv.1603.07179,
  title  = {Minuscule weights and Chevalley groups},
  author = {Meinolf Geck},
  journal= {arXiv preprint arXiv:1603.07179},
  year   = {2016}
}

Comments

18 pages; minor corrections

R2 v1 2026-06-22T13:17:00.819Z