On the combinatorial invariance of Kazhdan-Lusztig polynomials

We prove that the Kazhdan-Lusztig polynomials are combinatorial invariants for intervals up to length 8 in Coxeter groups of type A and up to length 6 in Coxeter groups of type B and D. As a consequence of our methods, we also obtain a complete classification, up to isomorphism, of Bruhat intervals of length 7 in type A and of length 5 in types B and D, which are not lattices. R

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Federico Incitti
• Keywords: Combinatorial Invariants, Coxeter Groups, JCT 2006, Les Groupes