5 research outputs found
A simple characterization of special matchings in lower Bruhat intervals
We give a simple characterization of special matchings in lower Bruhat
intervals (that is, intervals starting from the identity element) of a Coxeter
group. As a byproduct, we obtain some results on the action of special
matchings.Comment: accepted for publication on Discrete Mathematic
A simple characterization of special matchings in lower Bruhat intervals
We give a simple characterization of special matchings in lower Bruhat
intervals (that is, intervals starting from the identity element) of a Coxeter
group. As a byproduct, we obtain some results on the action of special
matchings.Comment: accepted for publication on Discrete Mathematic
The combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials of lower intervals
The aim of this work is to prove a conjecture related to the Combinatorial
Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting,
for lower intervals in every arbitrary Coxeter group. This result improves and
generalizes, among other results, the main results of [Advances in Math. {202}
(2006), 555-601], [Trans. Amer. Math. Soc. {368} (2016), no. 7, 5247--5269].Comment: to appear in Advances in Mathematic
Pircon kernels and up-down symmetry
We show that a symmetry property that we call the up-down symmetry implies
that the Kazhdan--Lusztig -polynomials of a pircon are a -kernel,
and we show that this property holds in the classical cases. Then, we enhance
and extend to this context a duality of Deodhar in parabolic Kazhdan--Lusztig
theory.Comment: to appear in Journal of Algebra. arXiv admin note: substantial text
overlap with arXiv:1907.0085