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

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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https://hal.archives-ouvertes.fr/hal-01691407
Contributor : Cédric Lecouvey <>
Submitted on : Monday, January 27, 2020 - 4:23:16 PM
Last modification on : Wednesday, January 29, 2020 - 1:37:36 AM

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  • HAL Id : hal-01691407, version 2
  • ARXIV : 1801.08313

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Cédric Lecouvey, Pierre Tarrago. Alcove random walks, k-Schur functions and the minimal boundary of the k-bounded partition poset. 2020. ⟨hal-01691407v2⟩

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