Counting semisimple orbits of finite Lie algebras by genus

Details Counting semisimple orbits of finite Lie algebras by genus Counting semisimple orbits of finite Lie algebras by genus

1997-12-12

arxiv.org/abs/math/9712246v2

Mathematics

Group Theory

Final galley version

Scientific paper

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.

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