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2002 Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups
Fokko du Cloux
Experiment. Math. 11(3): 371-381 (2002).


Let (W,S) be an arbitrary Coxeter system, {\small $y\in S^*$}. We describe an algorithm which will compute, directly from {\small $y$} and the Coxeter matrix of W, the interval from the identity to {\small $y$} in the Bruhat ordering, together with the (partially defined) left and right actions of the generators. This provides us with exactly the data that are needed to compute the Kazhdan-Lusztig polynomials {\small $P_{x,z}$, $x\leq z\leq y$}. The correctness proof of the algorithm is based on a remarkable theorem due to Matthew Dyer.


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Fokko du Cloux. "Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups." Experiment. Math. 11 (3) 371 - 381, 2002.


Published: 2002
First available in Project Euclid: 9 July 2003

zbMATH: 1101.20304
MathSciNet: MR1959749

Primary: 20C08
Secondary: 20C40 , 20F55 , 68R15

Keywords: computational group theory , Kazhdan-Lusztig polynomials

Rights: Copyright © 2002 A K Peters, Ltd.

Vol.11 • No. 3 • 2002
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