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Computing Kazhdan-Lusztig polynomials for arbitrary Coxeter groups. (English) Zbl 1101.20304

Summary: Let \((W,S)\) be an arbitrary Coxeter system, \(y\in S^*\). We describe an algorithm which will compute, directly from \(y\) and the Coxeter matrix of \(W\), the interval from the identity to \(y\) 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 \(P_{x,z}\), \(x\leq z\leq y\). The correctness proof of the algorithm is based on a remarkable theorem due to Matthew Dyer.

MSC:

20F55 Reflection and Coxeter groups (group-theoretic aspects)
05E15 Combinatorial aspects of groups and algebras (MSC2010)
20C40 Computational methods (representations of groups) (MSC2010)
68W30 Symbolic computation and algebraic computation

Software:

Coxeter
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References:

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