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Nonsymmetric Cauchy kernel, crystals and last passage percolation

Olga Azenhas, Thomas Gobet and Cédric Lecouvey
Vol. 6 (2024), No. 2, 249–297
DOI: 10.2140/tunis.2024.6.249
Abstract

We use nonsymmetric Cauchy kernel identities to get the law of last passage percolation models in terms of Demazure characters. The construction is based on some restrictions of the RSK correspondence that we rephrase in a unified way which is compatible with crystal basis theory.

Keywords
crystals, last passage percolation, RSK correspondence, Demazure characters, Cauchy identity
Mathematical Subject Classification
Primary: 05E10
Secondary: 05E05, 60K35
Milestones
Received: 3 June 2023
Accepted: 27 November 2023
Published: 29 June 2024
Authors
Olga Azenhas
CMUC
Department of Mathematics
University of Coimbra
Coimbra
Portugal
Thomas Gobet
Institut Denis Poisson, CNRS UMR 7013
Faculté des Sciences et Techniques
Université de Tours
Tours
France
Cédric Lecouvey
Institut Denis Poisson, CNRS UMR 7013
Faculté des Sciences et Techniques
Université de Tours
Tours
France
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