Abstract

Kazhdan–Lusztig polynomials have been proven to play an important role in different fields. Despite this, there are still few explicit formulae for them. Here we give closed product formulae for the Kazhdan–Lusztig polynomials indexed by Boolean elements in a class of Coxeter systems that we call linear. Boolean elements are elements smaller than a reflection that admits a reduced expression of the form s 1 … s n − 1 s n s n − 1 … s 1 ( s i ∈ S , s i ≠ s j if i ≠ j ). Then we provide several applications of this result concerning the combinatorial invariance of the Kazhdan–Lusztig polynomials, the classification of the pairs ( u , v ) with u ≺ v , the Kazhdan–Lusztig elements and the intersection homology Poincaré polynomials of the Schubert varieties.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.