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The most singular loci of twisted character varieties

  • Cheng Shu
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Abstract

For any simply connected almost simple group G and any compact Riemann surface of genus g>1, we study the singular locus of the character variety which parametrises fundamental group representations with a twist by a central element z of G. While for z=1 the most singular representations have values in a maximal torus (and are invariant for the Weyl group action) and for generic z every z-twisted representation is irreducible, for a general z we find that the most singular representations have values in a particular Levi subgroup Lz up to conjugation. From the explicit Lie-theoretic description of Lz, we determine the structure of the maximal stabiliser groups, and prove that the most singular loci is a disjoint union of generic type A character varieties.

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Cite

BibTeXRIS
BibTeX
@misc{shu2026most,
  title = {{The most singular loci of twisted character varieties}},
  author = {Cheng Shu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01528},
  eprint = {2611.01528},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01528},
}
RIS
TY  - UNPB
TI  - The most singular loci of twisted character varieties
AU  - Cheng Shu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01528
UR  - https://arxiv.org/abs/2611.01528
AB  - For any simply connected almost simple group G and any compact Riemann surface of genus g>1, we study the singular locus of the character variety which parametrises fundamental group representations with a twist by a central element z of G. While for z=1 the most singular representations have values in a maximal torus (and are invariant for the Weyl group action) and for generic z every z-twisted representation is irreducible, for a general z we find that the most singular representations have values in a particular Levi subgroup L_z up to conjugation. From the explicit Lie-theoretic description of L_z, we determine the structure of the maximal stabiliser groups, and prove that the most singular loci is a disjoint union of generic type A character varieties.
ER  -