Semi-continuit\'e des cellules de Kazhdan-Lusztig

TL;DR

This paper explores the semi-continuity phenomenon of Kazhdan-Lusztig cells with unequal parameters in Coxeter groups, aiming to establish a rigorous theoretical framework and formulate precise conjectures.

Contribution

It provides a theoretical foundation for the semi-continuity behavior of Kazhdan-Lusztig cells with unequal parameters and proposes new conjectures.

Findings

Computational evidence suggests semi-continuity in small Coxeter groups.

Formulation of precise conjectures on the behavior of cells with varying parameters.

Abstract

Computations in small Coxeter groups and infinite dihedral groups suggest that Kazhdan-Lusztig cells for unequal parameters obey to some "semicontinuity" phenomenon (as the parameter vary). The aim of this paper is to provide a rigorous theoretical background that allows to state some precise conjectures.