Disconnected Reductive Groups: Classification and Representations

Abstract

In this article, we classify (up to isomorphism) disconnected reductive groups over an algebraically closed field. For the fixed dimension and number of components, our results show that there are only finitely many reductive groups of that dimension with that many components. Besides this, we obtain new results about the structure and representation theory of disconnected reductive groups.

Version 2: improved exposition, minor issues fixed