## Experimental Mathematics

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

### Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups

#### 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