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
;
2017-01-01
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.File in questo prodotto:
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