Combinatorial representation theory and interactions with probabilistic models – CORTIPOM
This project aims to study and further develop combinatorial objects appearing in the representation theory of Coxeter groups, Lie algebras or their generalizations (complex reflections groups, Kac-Moody algebras), and simultaneously, to use them for investigating discrete probabilistic models and their connections with problems in mathematical physics. There are numerous interactions between models of these types based on the combinatorics of partitions (conditioning random walks, percolation problems, Tasep, card shuffling, cut-off phenomenon). The aim this project is to develop these interactions by using new results and objects that were introduced recently in representation theory (crystal graphs, shifted Schur functions, Hall-Littlewood and Macdonald polynomials, basic sets, generalizations of the RSK-procedure etc.). One of the original features of this project is to propose a unified approach to these different themes.
Project coordination
Cédric Lecouvey (UMR 7013 Institut Denis Poisson)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
Partner
LPSM Laboratoire de Probabilités, Statistiques et Modélisations
IDP UMR 7013 Institut Denis Poisson
Help of the ANR 260,032 euros
Beginning and duration of the scientific project:
January 2022
- 48 Months