Pietro Mongelli - Kazhdan-Lusztig polynomials of boolean elements

dmtcs:2326 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2326
Kazhdan-Lusztig polynomials of boolean elementsArticle

Authors: Pietro Mongelli 1

  • 1 Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type $q$ in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J. Algebra 295 (2006)], in Coxeter groups whose Coxeter graph is a tree. Such formulas involve Catalan numbers and use a combinatorial interpretation of the Coxeter graph of the group. In the case of classical Weyl groups, this combinatorial interpretation can be restated in terms of statistics of (signed) permutations. As an application of the formulas, we compute the intersection homology Poincaré polynomials of the Schubert varieties of boolean elements.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Coxeter groups,Kazhdan―Lusztig polynomials,Boolean elements,Poincaré polynomials,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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