We prove a duality result for the parabolic Kazhdan-Lusztig R-polynomials of a finite Coxeter system. This duality is similar to, but different from, the one obtained in [J. Douglass, Comm. Algebra, 18 (1990), 371-387.]. As a consequence of our duality we obtain an identity between the parabolic Kazhdan-Lusztig and inverse Kazhdan-Lusztig polynomials of a finite Coxeter system. We also obtain applications to certain modules defined by Deodhar and derive a result that gives evidence in favor of Marietti's combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials.

Brenti, F. (2017). A twisted duality for parabolic Kazhdan–Lusztig R-polynomials. JOURNAL OF ALGEBRA, 477(1), 472-482 [10.1016/j.jalgebra.2017.01.020].

A twisted duality for parabolic Kazhdan–Lusztig R-polynomials

Francesco Brenti
2017-01-01

Abstract

We prove a duality result for the parabolic Kazhdan-Lusztig R-polynomials of a finite Coxeter system. This duality is similar to, but different from, the one obtained in [J. Douglass, Comm. Algebra, 18 (1990), 371-387.]. As a consequence of our duality we obtain an identity between the parabolic Kazhdan-Lusztig and inverse Kazhdan-Lusztig polynomials of a finite Coxeter system. We also obtain applications to certain modules defined by Deodhar and derive a result that gives evidence in favor of Marietti's combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
English
Con Impact Factor ISI
Coxeter group; Parabolic Kazhdan–Lusztig polynomial; Parabolic R-polynomial;
Coxeter group; Parabolic R-polynomial; Parabolic Kazhdan–Lusztig polynomial;
https://www.sciencedirect.com/science/article/pii/S0021869317300431?via=ihub
https://www.mat.uniroma2.it/~brenti/54.pdf
Brenti, F. (2017). A twisted duality for parabolic Kazhdan–Lusztig R-polynomials. JOURNAL OF ALGEBRA, 477(1), 472-482 [10.1016/j.jalgebra.2017.01.020].
Brenti, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/225771
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