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Abstract : |
Abstract. We consider a class of random walks on a lattice, introduced by Gessel and Zeilberger, for which the reflection principle can be used to count the number of k-step walks between two points which stay within a chamber of a Weyl group. We prove three independent results about such "reflectable walks": first, a classification of all such walks; second, many determinant formulas for walk-numbers and their generating functions; third, an equality between the walk-numbers and the multiplicities of irreducibles in the kth tensor power of certain Lie group representations associated to the walk-types. Our results apply to the defining representations of the classical groups, as well as some spin representations of the orthogonal groups. 1, |
