Semicontinuity properties of Kazhdan-Lusztig cells
C\'edric Bonnaf\'e (LM-Besan\c{c}on)
TL;DR
This paper explores the semicontinuity properties of Kazhdan-Lusztig cells in Coxeter groups with unequal parameters, aiming to formalize conjectures based on computational observations.
Contribution
It provides a rigorous theoretical framework supporting the conjectured semicontinuity phenomena in Kazhdan-Lusztig cells with unequal parameters.
Findings
Supports conjectures with theoretical foundations
Formalizes semicontinuity behavior in cell partitions
Lays groundwork for future proofs
Abstract
Computations in small Coxeter groups or dihedral groups suggest that the partition into Kazhdan-Lusztig cells with unequal parameters should obey to some semicontinuity phenomenon (as the parameters vary). The aim of this paper is to provide a rigorous theoretical background for supporting this intuition that will allow to state several precise conjectures.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Combinatorial Mathematics