Equivariant Log Concavity and Representation Stability

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

doi:10.1093/imrn/rnab352

Equivariant Log Concavity and Representation Stability

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

Department of Mathematical Sciences

University of Bonn
Max Planck Institute for Mathematics
University of Oregon

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 s l n, we exploit the theory of representation stability to give computer-assisted proofs of these conjectures in low degree.

Original language	English
Pages (from-to)	3885-3906
Number of pages	22
Journal	International Mathematics Research Notices
Volume	2023
Issue number	5
DOIs	https://doi.org/10.1093/imrn/rnab352
State	Published - 1 Mar 2023

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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 s l n, we exploit the theory of representation stability to give computer-assisted proofs of these conjectures in low degree.",

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N2 - 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 s l n, we exploit the theory of representation stability to give computer-assisted proofs of these conjectures in low degree.

AB - 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 s l n, we exploit the theory of representation stability to give computer-assisted proofs of these conjectures in low degree.

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JO - International Mathematics Research Notices

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Equivariant Log Concavity and Representation Stability

Abstract

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