On the Genus number of Algebraic groups

Abstract

We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action of these groups on their Lie algebras. We also prove that the genus number of a connected reductive algebraic group coincides with the genus number of its semisimple part.

36 pages

References in corpus (1)

• Conjugacy Classes of Centralizers in $G_2$

Cited by in corpus (1)

• Computations in Classical Groups