2024/10/07 by Auguste Hébert, Hébert, Auguste, Paul Philippe +1
Mathematics · #Geometric and Algebraic Topology #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2410.04872
In 2019, D. Muthiah proposed a strategy to define affine Kazhdan-Lusztig R-polynomials for Kac-Moody groups. Since then, Bardy-Panse, the first author and Rousseau have introduced the formalism of twin masures and the authors have extended combinatorial results from affine root systems to general Kac-Moody root systems in a previous article. In this paper, we use these results to explicitly define affine R-Kazhdan-Lusztig polynomials for Kac-Moody groups. The construction is based on a path model lifting to twin masures. Conjecturally, these polynomials count the cardinality of intersections of opposite affine Schubert cells, as in the case of reductive groups.