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.

Brenti, F., & Caselli, F. (2017). Peak algebras, paths in the Bruhat graph and Kazhdan–Lusztig polynomials. ADVANCES IN MATHEMATICS, 304, 539-582 [10.1016/j.aim.2016.09.001].

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

Brenti Francesco
;
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.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - Algebra
English
Con Impact Factor ISI
Quasi-symmetric functions; Coxeter groups; Reflection orderings; Kazhdan-Lusztig polynomials
dx.doi.org/10.1016/j.aim.2016.09.001
www.mat.uniroma2.it/~brenti/50.pdf
Brenti, F., & Caselli, F. (2017). Peak algebras, paths in the Bruhat graph and Kazhdan–Lusztig polynomials. ADVANCES IN MATHEMATICS, 304, 539-582 [10.1016/j.aim.2016.09.001].
Brenti, F; Caselli, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/191782
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