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More on the combinatorial invariance of Kazhdan-Lusztig polynomials. (English) Zbl 1117.05109

Summary: 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.

MSC:

05E15 Combinatorial aspects of groups and algebras (MSC2010)
20F55 Reflection and Coxeter groups (group-theoretic aspects)

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References:

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