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I am reading the paper Masato Kobayashi---Combinatorics on Bruhat Graphs and Kazhdan-Lusztig Polynomials.

Let $P_{x,w}$ be the Kazhdan Lusztig polynomial of $W$. There is a result about crystallographic Coxeter group $W$: enter image description here

I would like to know whether there is any generalization of this result to a larger class of Coxeter groups which has been proven up to now?

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  • $\begingroup$ Keep in mind the fact that the known result aready covers all cases in which the group is a "Weyl group", though your question is a natural one to raise. (By the way, I just expanded the tags and fixed a couple of small linguistic errors.) $\endgroup$ – Jim Humphreys Sep 19 '19 at 12:47

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