Algebraic groups and $G$-complete reducibility: a geometric approach

Benjamin Martin* (Corresponding Author)

*Corresponding author for this work

Research output: Working paperPreprint

Abstract

The notion of a \emph{$G$-completely reducible} subgroup is important in the study of algebraic groups and their subgroup structure. It generalizes the usual idea of complete reducibility from representation theory: a subgroup $H$ of a general linear group $G= {\rm GL}_n(k)$ is $G$-completely reducible if and only if the inclusion map $i\colon H\rightarrow {\rm GL}_n(k)$ is a completely reducible representation of $H$. In these notes I give an introduction to the theory of complete reducibility and its applications, and explain an approach to the subject using geometric invariant theory.
Original languageEnglish
PublisherArXiv
Number of pages28
DOIs
Publication statusPublished - 25 Jul 2022

Fingerprint

Dive into the research topics of 'Algebraic groups and $G$-complete reducibility: a geometric approach'. Together they form a unique fingerprint.

Cite this