Counting Semisimple Orbits of Finite Lie Algebras by Genus
- Publisher: Elsevier BV
Journal of Algebra,
17B45 | Mathematics - Combinatorics | 20G40 | Algebra and Number Theory | Mathematics - Group Theory
The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are obtained for other types. For type A a probabilistic interpretation is given in terms of card shuffling.