Equivariant log concavity and representation stability
Combinatorics
2021-11-01 v2 Representation Theory
Abstract
We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In the case of the Coxeter arrangement for the Lie algebra , we exploit the theory of representation stability to give computer assisted proofs of these conjectures in low degree.
Cite
@article{arxiv.2104.00715,
title = {Equivariant log concavity and representation stability},
author = {Jacob P. Matherne and Dane Miyata and Nicholas Proudfoot and Eric Ramos},
journal= {arXiv preprint arXiv:2104.00715},
year = {2021}
}