Semicontinuity properties of Kazhdan-Lusztig cells

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.

29 pages. The paper arXiv:0805.3038 has been divided in two parts. This paper is an enriched (and translated) version of sections 1, 4, 5, 6 and 7 of arXiv:0805.3038

References in corpus (6)

• Hecke algebras with unequal parameters
• On the cyclotomic Hecke algebras of complex reflection groups
• Blocks and families for cyclotomic Hecke algebras
• Left cells in type $B_n$ with unequal parameters
• Cells and Constructible Representations in type B
• Topologie sur l'ensemble des parties positives d'un réseau

Cited by in corpus (8)

• Two boundary Hecke Algebras and combinatorics of type C
• A proof of Lusztig's conjectures for affine type $G_2$ with arbitrary parameters
• Hecke algebras and symplectic reflection algebras
• Some applications of CHEVIE to the theory of algebraic groups
• Schur elements and basic sets for cyclotomic Hecke algebras
• Conjectures P1-P15 for hyperbolic Coxeter groups of rank 3
• Asymptotic lowest two-sided cell
• Affine cellularity of affine Hecke algebras of rank two