{
  "abstract": "We study the universal central extensions of the derivation and current algebras of a superelliptic curve $u^m=P(x)$, for $P$ palindromic of degree $2r$. Both centres are finite-dimensional and canonically isomorphic. On the derivation side the dimension is known at every covering degree, while reducing an arbitrary class has been done only for the double cover $m=2$; we do it at every $m$. The spanning classes split into $r(m-1)$ chains, each an associated ultraspherical family whose parameters come from the sector and the residue, and we determine which chains carry a positive orthogonality measure. For quadratic $P$ we evaluate the mixed cocycle in closed form, as a combination of two Legendre antiderivatives, at every pair of generators of total index at least three.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.02530",
  "author_total": 1,
  "authors": [
    {
      "name": "Felipe Albino dos Santos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/46tz74ed4zw2t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.02530",
  "fulltext_url": null,
  "id": "46tz74ed4zw2t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.02530",
  "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.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7160274001",
  "pdf_url": "https://arxiv.org/pdf/2605.02530",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/46tz74ed4zw2t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2605.02530",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.02530"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Orthogonal polynomials and the centres of the universal central extensions of superelliptic Krichever--Novikov algebras",
  "title_text": "Orthogonal polynomials and the centres of the universal central extensions of superelliptic Krichever--Novikov algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/46tz74ed4zw2t",
  "venue": "arXiv",
  "versions": []
}