Semisimple Orbits of Lie Algebras and Card-shuuing Measures on Coxeter Groups
نویسنده
چکیده
Random walk on the chambers of hyperplanes arrangements is used to de ne a family of card shu ing measuresMW;x for a nite Coxeter group W and real x 6= 0. By algebraic group theory, there is a map from the semisimple orbits of the adjoint action of a nite group of Lie type on its Lie algebra to the conjugacy classes of the Weyl group. Choosing such a semisimple orbit uniformly at random thereby induces a probability measure on the conjugacy classes of the Weyl group. It is conjectured that for q good and regular, this measure on conjugacy classes is equal to the measure arising fromMW;q. This conjecture is veri ed for all types for the identity conjugacy class, and is con rmed for all conjugacy classes for types A and B.
منابع مشابه
Semisimple Orbits of Lie Algebras and Card-shuffling Measures on Coxeter Groups
Solomon’s descent algebra is used to define a family of signed measures MW,x for a finite Coxeter group W and x > 0. The measures corresponding to W of type An arise from the theory of card shuffling. Formulas for these measures are obtained and conjectured in special cases. The eigenvalues of the associated Markov chains are computed. By elementary algebraic group theory, choosing a random sem...
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