Year: 2016
Type: preprint
Abstract: The traditional construction of Chevalley groups relies on the choice of certain signs for a Chevalley basis of the underlying Lie algebra~$\mathfrak{g}$. Recently, Lusztig simplified this construction for groups of adjoint type by using the "canonical basis" of the adjoint representation of~$\mathfrak{g}$, 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~$\mathfrak{g}$.
Source: arXiv (Cornell University)
Author: Geck, Meinolf
Institution: University of Stuttgart
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G155831931
OpenAlex ID: W4301808107