Equivariant log concavity and representation stability

2021/04/01 by Jacob P. Matherne, Dane Miyata, Matherne, Jacob P. +5
Mathematics · #05B35 (Primary) 14N20 #20F55 #55N33 #55R80 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05B35 #msc:14N20 #msc:20F55 #msc:55N33 #msc:55R80

paper · pdf · doi:10.48550/arxiv.2104.00715

arxiv created 2021/10/29 · arxiv updated 2021/11/01

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 \mathfraksl_n, we exploit the theory of representation stability to give computer assisted proofs of these conjectures in low degree.

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