More on the combinatorial invariance of Kazhdan--Lusztig polynomials

Authors:
Federico Incitti
Affiliations:
Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 4
Cited 1

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Bruhat intervals as rooks on skew Ferrers boards

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Abstract

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.