Counting Semisimple Orbits of Finite Lie Algebras by Genus

Article, Preprint English OPEN
Fulman, Jason (1999)
  • Publisher: Elsevier BV
  • Journal: Journal of Algebra, volume 217, issue 1, pages 170-179 (issn: 0021-8693)
  • Related identifiers: doi: 10.1006/jabr.1998.7805
  • Subject: 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.
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