Counting Semisimple Orbits of Finite Lie Algebras by Genus
نویسنده
چکیده
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 semisimple orbits of a given split 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.
منابع مشابه
Counting Split Semisimple Orbits of Finite Lie Algebras by Genus
The adjoint action of a nite 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 Solomon's descent algebra and card shu ing. 3
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