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PreprintarXiv licencearXiv

PGL2 webs at roots of unity

  • Vijay Higgins
  • Bryan Silva
  • Amy Somers
  • David Stephens
  • Srijan Sundar
  • Parth Wokhlu
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Abstract

We study webs on surfaces for the PGL2 skein theory specialized at roots of unity. We construct the PGL2 analogue of Chebyshev polynomials and use them to construct central elements in the skein algebra. We then focus on the cases of the 3-punctured sphere and the closed torus. We compute the Frobenius homomorphism for these two surfaces and show that the PGL2 Frobenius homomorphism for the torus is not injective when the quantum parameter q2 is a root of unity of even order n.

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Cite

BibTeXRIS
BibTeX
@misc{higgins2026pgl2,
  title = {{$\rmPGL_2$ webs at roots of unity}},
  author = {Vijay Higgins and Bryan Silva and Amy Somers and David Stephens and Srijan Sundar and Parth Wokhlu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01881},
  eprint = {2610.01881},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01881},
}
RIS
TY  - UNPB
TI  - PGL_2 webs at roots of unity
AU  - Vijay Higgins
AU  - Bryan Silva
AU  - Amy Somers
AU  - David Stephens
AU  - Srijan Sundar
AU  - Parth Wokhlu
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01881
UR  - https://arxiv.org/abs/2610.01881
AB  - We study webs on surfaces for the PGL_2 skein theory specialized at roots of unity. We construct the PGL_2 analogue of Chebyshev polynomials and use them to construct central elements in the skein algebra. We then focus on the cases of the 3-punctured sphere and the closed torus. We compute the Frobenius homomorphism for these two surfaces and show that the PGL_2 Frobenius homomorphism for the torus is not injective when the quantum parameter q^2 is a root of unity of even order n.
ER  -