Alcove random walks, k-Schur functions and the minimal boundary of the k-bounded partition poset
| Autor: | Pierre Tarrago, Cédric Lecouvey |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
010102 general mathematics
Boundary (topology) Affine Grassmannian (manifold) Random walk 01 natural sciences Toeplitz matrix Combinatorics 010104 statistics & probability Bounded function Discrete Mathematics and Combinatorics Partition (number theory) 0101 mathematics Mathematics::Representation Theory Partially ordered set Mathematics Quantum cohomology |
| Zdroj: | Algebraic Combinatorics. 4:241-272 |
| ISSN: | 2589-5486 |
| DOI: | 10.5802/alco.147 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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