Equivariant log concavity and representation stability

Matherne, Jacob P.; Miyata, Dane; Proudfoot, Nicholas; Ramos, Eric

doi:10.1093/imrn/rnab352

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Equivariant log concavity and representation stability

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Matherne, Jacob P.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1093/imrn/rnab352
(Publisher version)

https://arxiv.org/abs/2104.00715
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Citation

Matherne, J. P., Miyata, D., Proudfoot, N., & Ramos, E. (2023). Equivariant log concavity and representation stability. International Mathematics Research Notices, 2023(5), 3885-3906. doi:10.1093/imrn/rnab352.

Cite as: https://hdl.handle.net/21.11116/0000-000A-21FF-2

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
$\mathfrak{sl}_n$, we exploit the theory of representation stability to give
computer assisted proofs of these conjectures in low degree.