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PreprintCC BY 4.0arXiv

Orthogonal polynomials and the centres of the universal central extensions of superelliptic Krichever--Novikov algebras

  • Felipe Albino dos Santos
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Abstract

We study the universal central extensions of the derivation and current algebras of a superelliptic curve um=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.

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Cite

BibTeXRIS
BibTeX
@misc{santos2026orthogonal,
  title = {{Orthogonal polynomials and the centres of the universal central extensions of superelliptic Krichever--Novikov algebras}},
  author = {Felipe Albino dos Santos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.02530},
  eprint = {2605.02530},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.02530},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Orthogonal polynomials and the centres of the universal central extensions of superelliptic Krichever--Novikov algebras
AU  - Felipe Albino dos Santos
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2605.02530
UR  - https://arxiv.org/abs/2605.02530
AB  - 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.
ER  -