Kazhdan-Lusztig combinatorics via sheaves on Bruhat graphs

preprint2006arXivOpen access

Abstract

We study the projective objects in an exact category naturally associated to a Coxeter system. We discuss an analog of the Kazhdan-Lusztig conjecture and show how it follows from a "genericity" conjecture and how the latter follows from a "Hard Lefschetz" conjecture.

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