{
  "abstract": "Let $G$ be a split reductive group defined over a field of characteristic bigger than the Coxeter numbers of its simple factors. We identify the Harish--Chandra centers of the associated Kac--Moody vertex algebras and enveloping algebras at noncritical levels with algebras of functions on moduli spaces of connections for the Langlands dual group $\\check{G}$. Namely, given a noncritical level $κ$ for $G$, consider the associated Kac--Moody vertex algebra $V_κ(\\mathfrak{g})$ defined on a formal disc $\\mathscr{D}$, and its Harish--Chandra center of arc group invariants $$V_κ(\\mathfrak{g})^{\\mathscr{J}G} \\subset V_κ(\\mathfrak{g}).$$ Write $\\checkκ$ for the dual level for $\\check{G}$, $\\checkκ^p - \\checkκ$ for its image under the Artin--Schreier map, and $\\operatorname{Op}_{\\check{G}}(\\mathscr{D}^{(1)})_{\\checkκ^p - \\checkκ}$ for the moduli space of $(\\checkκ^p - \\checkκ)$-opers on the Frobenius twisted disc $\\mathscr{D}^{(1)}$. We establish a canonical isomorphism $$\\operatorname{Spec} V_κ(\\mathfrak{g})^{\\mathscr{J} G} \\simeq \\operatorname{Op}_{\\check{G}}(\\mathscr{D}^{(1)})_{\\checkκ^p - \\checkκ}.$$ There is a similar identification for the Harish--Chandra center of the filtered complete enveloping algebra at level $κ$, where instead of $\\mathscr{D}$ we need to consider the punctured disc $\\mathscr{D}^\\times$. The presence of these Harish--Chandra centers is a genuinely new phenomenon for loop groups at noncritical level in positive characteristic: these centers are nontrivial, unlike for loop groups at noncritical level in characteristic zero, and in particular are not the reductions mod $p$ of the characteristic zero Harish--Chandra centers, unlike for finite dimensional reductive groups or loop groups at critical level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23560",
  "author_total": 2,
  "authors": [
    {
      "name": "Gurbir Dhillon"
    },
    {
      "name": "Ivan Losev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4yxqjwe38q1d9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23560",
  "fulltext_url": null,
  "id": "4yxqjwe38q1d9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23560",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214005403",
  "pdf_url": "https://arxiv.org/pdf/2609.23560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4yxqjwe38q1d9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23560"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Affine Harish-Chandra center in positive characteristic",
  "title_text": "Affine Harish-Chandra center in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4yxqjwe38q1d9",
  "venue": "arXiv",
  "versions": []
}