Shuffling cards and Lie theory

Jason E. Fulman

Dartmouth University

April 28,
refreshments at 3:45pm


Using the Bidigare-Hanlon-Rockmore theory of random walk on the chambers of hyperplane arrangements, we define a notion of riffle shuffling for any finite Coxeter group or real hyperplane arrangement. We show that in the Coxeter case the resulting probability measures relate to enumerative problems about conjugacy classes in the finite groups of Lie type (with restrictions on the characteristic related to how the root hyperplane arrangement reduces mod p). We give open problems and mention another connection of type A,B card shuffling with Lie theory, namely the Poincare-Birkhoff-Witt theorem and splittings of Hochschild homology.

Speaker's Contact Info: Jason.E.Fulman(at-sign)Dartmouth.EDU

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