Quasisymmetric functions and Kazhdan-Lusztig polynomials
By Louis J. Billera, Francesco Brenti. 2007
52 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Spectroscopy
View Paper: https://www.semanticscholar.org/paper/f100bdb8375810bbb583562228e5235fd2e757a7
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Citations in the corpus
- Modules of the 0-Hecke algebra and quasisymmetric Schur functions (2014, background): “They have also been seen to simplify many symmetric functions such as Macdonald polynomials [26, 27], Kazhdan-Lusztig polynomials [8] and identify equal ribbon Schur functions [10], as well as arising in category theory [2], topology [4, 25], and graph theory [15, 32, 51].”
- Skew quasisymmetric Schur functions and noncommutative Schur functions (2010, background): “oup [32]; investigate the behavior of random permutations [63]; in addition to simplifying the calculation of symmetric functions such as Macdonald polynomials [28, 29] and Kazhdan-Lustig polynomials [12]. Dual to QSym is a noncommutative analogue NSym, the Hopf algebra of noncommutative symmetric f”