A note on Combinatorial Invariance of Kazhdan--Lusztig polynomials
Combinatorics
2024-11-27 v3 Representation Theory
Abstract
We introduce the concepts of an amazing hypercube decomposition and a double shortcut for it, and use these new ideas to formulate a conjecture implying the Combinatorial Invariance Conjecture of the Kazhdan--Lusztig polynomials for the symmetric group. This conjecture has the advantage of being combinatorial in nature. The appendix by Grant T. Barkley and Christian Gaetz discusses the related notion of double hypercubes and proves an analogous conjecture for these in the case of co-elementary intervals.
Keywords
Cite
@article{arxiv.2404.12834,
title = {A note on Combinatorial Invariance of Kazhdan--Lusztig polynomials},
author = {Francesco Esposito and Mario Marietti and Grant T. Barkley and Christian Gaetz},
journal= {arXiv preprint arXiv:2404.12834},
year = {2024}
}