We give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the Kazhdan–Lusztig polynomials which holds in complete generality and is simpler and more explicit than any existing one. We point out that, in a certain sense, this formula cannot be simplified.

Peak algebras, paths in the Bruhat graph and Kazhdan–Lusztig polynomials / Brenti, Francesco; Caselli, Fabrizio. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 304:(2017), pp. 539-582. [10.1016/j.aim.2016.09.001]

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

CASELLI, FABRIZIO
2017

Abstract

We give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the Kazhdan–Lusztig polynomials which holds in complete generality and is simpler and more explicit than any existing one. We point out that, in a certain sense, this formula cannot be simplified.
2017
Peak algebras, paths in the Bruhat graph and Kazhdan–Lusztig polynomials / Brenti, Francesco; Caselli, Fabrizio. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 304:(2017), pp. 539-582. [10.1016/j.aim.2016.09.001]
Brenti, Francesco; Caselli, Fabrizio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/587501
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