Semisimple orbits of Lie algebras and card-shuffling measures on Coxeter groups

JOURNAL OF ALGEBRA

卷:224

Article

Fulman, J

关键词: card shuffling;    hyperplane arrangement;    conjugacy class;    adjoint action.;   

DOI  :  10.1006/jabr.1999.8157

来源: Elsevier

【 摘 要 】

Random walk on the chambers of hyperplane arrangements is used to define a family of card shuffling measures H-W,H-x for a finite Coxeter group W and real x not equal 0. By algebraic group theory, there is a map Phi from the semisimple orbits of the adjoint action of a finite 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. For types A, B, and the identity conjugacy class of W for all types, it is proved that for q very good, this measure on conjugacy classes is equal to the measure arising from H-W,H-q. The possibility of refining Phi to a map to elements of the Weyl group is discussed. (C) 2000 Academic Press.

【 授权许可】

Free