Quasisymmetric Functions and Kazhdan-lusztig Polynomials
نویسندگان
چکیده
We associate a quasisymmetric function to any Bruhat interval in a general Coxeter group. This association can be seen to be a morphism of Hopf algebras to the subalgebra of all peak functions, leading to an extension of the cd-index of convex polytopes. We show how the Kazhdan-Lusztig polynomial of the Bruhat interval can be expressed in terms of this complete cd-index and otherwise explicit combinatorially defined polynomials. In particular, we obtain the simplest closed formula for the Kazhdan-Lusztig polynomials that holds in complete generality.
منابع مشابه
Peak algebras , paths in the Bruhat graph and Kazhdan - Lusztig polynomials ∗
We obtain a nonrecursive combinatorial formula for the Kazhdan-Lusztig polynomials which holds in complete generality and which is simpler and more explicit than any existing one, and which cannot be linearly simplified. Our proof uses a new basis of the peak subalgebra of the algebra of quasisymmetric functions. Résumé. On montre une formule combinatoire pour les polynômes de Kazhdan-Lusztig q...
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