Francesco Brenti ; Fabrizio Caselli - Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

dmtcs:2423 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2423
Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

Authors: Francesco Brenti 1; Fabrizio Caselli 2

  • 1 Università degli Studi di Roma Tor Vergata [Roma]
  • 2 Alma Mater Studiorum Università di Bologna [Bologna]

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.

https://doi.org/10.46298/dmtcs.2423
Source: HAL:hal-01207552v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: lattice paths,Coxeter groups,cd-index,quasi-symmetric functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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