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Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

Abstract : 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.
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Francesco Brenti, Fabrizio Caselli. Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.561-572. ⟨hal-01207552⟩

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