Alcove random walks, k-Schur functions and the minimal boundary of the k-bounded partition poset

2018/01/25 by Lecouvey, Cédric, Tarrago, Pierre
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1801.08313

Abstract

We use k-Schur functions to get the minimal boundary of the k-bounded partition poset. This permits to describe the central random walks on affine Grassmannian elements of type A and yields a polynomial expression for their drift. We also recover Rietsch's parametriza-tion of totally nonnegative unitriangular Toeplitz matrices without using quantum cohomology of flag varieties. All the homeomorphisms we define can moreover be made explicit by using the combinatorics of k-Schur functions and elementary computations based on Perron-Frobenius theorem.

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