Quasisymmetric functions and Kazhdan-Lusztig polynomials
- Resource Type
- Working Paper
- Authors
- Billera, Louis J.; Brenti, Francesco
- Source
- Subject
- Mathematics - Combinatorics
Mathematics - Representation Theory
20F55, 05E99 (Primary)
05E15 (Secondary)
- Language
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.
Comment: 27 pages. Final version: definitions reorganized for clarity, added Example 4.6 and two citations. To appear in Israel Journal of Mathematics