Modular law through GKM theory
Algebraic Topology
2023-10-26 v1 Algebraic Geometry
Combinatorics
Representation Theory
Abstract
The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot action. A similar result holds between unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties. A recent result by Abreu-Nigro enabled us to prove these results by showing the modular law for the geometrical objects, and this is indeed done by Precup-Sommers and Kiem-Lee. In this paper, we give elementary and simpler proofs to the modular law through GKM theory.
Cite
@article{arxiv.2310.16235,
title = {Modular law through GKM theory},
author = {Tatsuya Horiguchi and Mikiya Masuda and Takashi Sato},
journal= {arXiv preprint arXiv:2310.16235},
year = {2023}
}
Comments
17 page, 5 figures