Equivariant log concavity and representation stability

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 \(\...

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Bibliographic Details
Published in:arXiv.org 2021-10
Main Authors: Matherne, Jacob P, Miyata, Dane, Proudfoot, Nicholas, Ramos, Eric
Format: Article
Language:English
Subjects:
Algebra
Concavity
Hyperplanes
Lie groups
Representations
Stability
Online Access:Get full text
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Summary: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 \(\mathfrak{sl}_n\), we exploit the theory of representation stability to give computer assisted proofs of these conjectures in low degree.
ISSN:2331-8422