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Journal of the Ramanujan Mathematical Society

Volume 28, Issue 4, December 2013  pp. 443–482.

On the genus number of algebraic groups

Authors Anirban Bose
Author institution: Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi 110 016, India

Summary:  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 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.

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