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
2016-01-01
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.File in questo prodotto:
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