Borel–de Siebenthal theory

Borel–de Siebenthal theory is a mathematical framework primarily associated with the study of compact Lie groups and their representations, particularly in the context of algebraic groups and symmetric spaces. The theory deals with the classification of maximal connected solvable subgroups, or Borel subgroups, in the context of semisimple Lie groups. It extends concepts of Borel subgroups from the language of algebraic groups to that of Lie groups.