{
  "id": "2202.08170",
  "version": "v1",
  "published": "2022-02-16T16:21:03.000Z",
  "updated": "2022-02-16T16:21:03.000Z",
  "title": "Faithfulness of generalised Verma modules for Iwasawa algebras",
  "authors": [
    "Stephen Mann"
  ],
  "categories": [
    "math.RT",
    "math.NT",
    "math.RA"
  ],
  "abstract": "We prove faithfulness of infinite-dimensional generalised Verma modules for Iwasawa algebras corresponding to split simple Lie algebras with a Chevalley basis. We use this to prove faithfulness of all infinite-dimensional highest-weight modules in the case of type $A_{2}$. In this case we also show that all prime ideals of the corresponding Iwasawa algebras are annihilators of finite-dimensional simple modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-16T16:21:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S99",
      "22E50",
      "16D25"
    ],
    "keywords": [
      "faithfulness",
      "split simple lie algebras",
      "infinite-dimensional generalised verma modules",
      "finite-dimensional simple modules",
      "infinite-dimensional highest-weight modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}