{
  "id": "2104.00715",
  "version": "v1",
  "published": "2021-04-01T18:47:38.000Z",
  "updated": "2021-04-01T18:47:38.000Z",
  "title": "Equivariant log concavity and representation stability",
  "authors": [
    "Jacob P. Matherne",
    "Dane Miyata",
    "Nicholas Proudfoot",
    "Eric Ramos"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-01T18:47:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "14N20",
      "20F55",
      "55N33",
      "55R80"
    ],
    "keywords": [
      "representation stability",
      "equivariant log concavity conjectures",
      "low degree",
      "cordovil algebras",
      "orlik-terao algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}