✦ LIBER ✦

Counting Semisimple Orbits of Finite Lie Algebras by Genus

✍ Scribed by Jason Fulman

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 82 KB
Volume: 217
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7805

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✦ Synopsis

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.

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Random walk on the chambers of hyperplane arrangements is used to define a family of card shuffling measures H W x for a finite Coxeter group W and real x = 0. By algebraic group theory, there is a map from the semisimple orbits of the adjoint action of a finite group of Lie type on its Lie algebra