{
  "abstract": "Let $G$ be a split connected reductive algebraic group over a non-archimedean local field $F$ of characteristic zero. The stable center conjecture asserts that the subspace of stable elements in the Bernstein center of $G(F)$ is a sub-algebra, and this subring is conjecturally isomorphic to the regular functions on the moduli of semi-simple Langlands parameters. Bezrukavnikov-Kazhdan-Varshavsky suggested an approach towards the stable center conjecture by explicitly constructing elements and proving their stability directly without assuming LLC, and proved the stability of the depth-$r$ projectors. Following the idea, the first author and Tsao-Hsien Chen produced a family of elements in the center which are conjecturally stable using Deligne-Lusztig parameters attached to irreducible representations. This paper proves the stability of the projectors corresponding to strongly regular Deligne-Lusztig parameters in depth-zero, and for all the positive depth elements with some restrictions on the residue characteristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33327",
  "author_total": 2,
  "authors": [
    {
      "name": "Sarbartha Bhattacharya"
    },
    {
      "name": "Shenghao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56rx9dbh3mqz2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33327",
  "fulltext_url": null,
  "id": "56rx9dbh3mqz2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33327",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223895615",
  "pdf_url": "https://arxiv.org/pdf/2610.33327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56rx9dbh3mqz2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Stability of certain elements in the Bernstein center",
  "title_text": "Stability of certain elements in the Bernstein center",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/56rx9dbh3mqz2",
  "venue": "arXiv",
  "versions": []
}