Alcove random walks, k-Schur functions and the minimal boundary of the k-bounded partition poset - Archive ouverte HAL Access content directly
Journal Articles Algebraic Combinatorics Year : 2021

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

Cédric Lecouvey
Pierre Tarrago
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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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Dates and versions

hal-01691407 , version 1 (24-01-2018)
hal-01691407 , version 2 (27-01-2020)

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Cédric Lecouvey, Pierre Tarrago. Alcove random walks, k-Schur functions and the minimal boundary of the k-bounded partition poset. Algebraic Combinatorics, 2021, 4 (2), pp.241-272. ⟨10.5802/alco.147⟩. ⟨hal-01691407v2⟩
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