arXiv math/97122461997-12math.GRmath.CO

Counting semisimple orbits of finite Lie algebras by genus

Jason Fulman

备注：: Final galley version

英文摘要：

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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