Experimental Mathematics

Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups

Fokko du Cloux

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Abstract

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.

Article information

Source
Experiment. Math., Volume 11, Issue 3 (2002), 371-381.

Dates
First available in Project Euclid: 9 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1057777429

Mathematical Reviews number (MathSciNet)
MR1959749

Zentralblatt MATH identifier
1101.20304

Subjects
Primary: 20C08: Hecke algebras and their representations
Secondary: 20C40: Computational methods 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 68R15: Combinatorics on words

Keywords
Kazhdan-Lusztig polynomials computational group theory

Citation

du Cloux, Fokko. Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups. Experiment. Math. 11 (2002), no. 3, 371--381. https://projecteuclid.org/euclid.em/1057777429


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