Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups

du Cloux, Fokko

du Cloux, Fokko

Experiment. Math., Tome 11 (2002) no. 3, p. 371-381 / Harvested from Project Euclid

Résumé

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.

Publié le : 2002-05-14
Classification: Kazhdan-Lusztig polynomials, computational group theory, 20C08, 20C40, 20F55, 68R15

@article{1057777429,
     author = {du Cloux, Fokko},
     title = {Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 371-381},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1057777429}
}

du Cloux, Fokko. Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups. Experiment. Math., Tome 11 (2002) no. 3, pp.  371-381. http://gdmltest.u-ga.fr/item/1057777429/