Shuffling cards and Lie theory
Jason E. Fulman
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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