{
  "id": "2307.12521",
  "version": "v1",
  "published": "2023-07-24T04:33:59.000Z",
  "updated": "2023-07-24T04:33:59.000Z",
  "title": "Steinberg's cross-section of Newton strata",
  "authors": [
    "Sian Nie"
  ],
  "comment": "18 pages. Comments welcome!",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We introduce a natural analogue of Steinberg's cross-section in the loop group of an unramified reductive group $\\mathbf G$. We show this loop Steinberg's cross-section provides a simple geometric model for the poset $B(\\mathbf G)$ of Frobenius-twisted conjugacy classes (referred to as Newton strata) of the loop group. As an application, we confirm a conjecture by Ivanov on loop Delgine-Lusztig varieties of Coxeter type. This geometric model also leads to new and direct proofs of several classical results, including the converse to Mazur's inequality, Chai's length formula on $B(\\mathbf G)$, and a key combinatorial identity in the study affine Deligne-Lusztig varieties with finite Coxeter parts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-24T04:33:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "newton strata",
      "loop group",
      "study affine deligne-lusztig varieties",
      "simple geometric model",
      "finite coxeter parts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}