We study the parabolic Kazhdan-Lusztig polynomials for the quasi-minuscule quotients of Weyl groups. We give explicit closed combinatorial formulas for the parabolic Kazhdan-Lusztig polynomials of type q. Our study implies that these are always either zero or a monic power of q, and that they are not combinatorial invariants. We conjecture a combinatorial interpretation for the parabolic Kazhdan-Lusztig polynomials of type -1.

Brenti, F., Mongelli, P., & Sentinelli, P. (2016). Parabolic Kazhdan-Lusztig polynomials for quasi-minuscule quotients. ADVANCES IN APPLIED MATHEMATICS, 78, 27-55 [10.1016/j.aam.2016.01.005].

Parabolic Kazhdan-Lusztig polynomials for quasi-minuscule quotients

BRENTI, FRANCESCO;SENTINELLI, PAOLO
2016

Abstract

We study the parabolic Kazhdan-Lusztig polynomials for the quasi-minuscule quotients of Weyl groups. We give explicit closed combinatorial formulas for the parabolic Kazhdan-Lusztig polynomials of type q. Our study implies that these are always either zero or a monic power of q, and that they are not combinatorial invariants. We conjecture a combinatorial interpretation for the parabolic Kazhdan-Lusztig polynomials of type -1.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - Algebra
English
Con Impact Factor ISI
Kazhdan-Lusztig polynomial; quasi-minuscule quotient; Weyl group; combinatorics
http://www.mat.uniroma2.it/~brenti/53.dvi
Brenti, F., Mongelli, P., & Sentinelli, P. (2016). Parabolic Kazhdan-Lusztig polynomials for quasi-minuscule quotients. ADVANCES IN APPLIED MATHEMATICS, 78, 27-55 [10.1016/j.aam.2016.01.005].
Brenti, F; Mongelli, P; Sentinelli, P
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/173645
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