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Weyl defects in skein theory and quantum cluster charts

  • Jennifer Brown
  • Juan Ramón Gómez García
  • David Jordan
  • Matthias Vancraeynest
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Abstract

We prove a modified invertibility property for the parabolic defects introduced in arXiv:2102.12283, arXiv:2505.14836. Namely, we show that the Borel defect cancels its dual, up to insertion of an invertible Weyl defect and up to restriction to an open-subcategory. The main result holds for an arbitrary reductive group G -- for illustration we give extended computations for G=SL3. Along the way, we introduce a defect skein theory with defects in both codimension one and two, which is compatible with gluing of defect 3-manifolds and defect surfaces. Our results provide a potential defect skein theoretic construction of certain standard charts which appears frequently in quantum cluster varieties associated to surfaces.

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Cite

BibTeXRIS
BibTeX
@misc{brown2026weyl,
  title = {{Weyl defects in skein theory and quantum cluster charts}},
  author = {Jennifer Brown and Juan Ramón Gómez García and David Jordan and Matthias Vancraeynest},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09308},
  eprint = {2609.09308},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09308},
}
RIS
TY  - UNPB
TI  - Weyl defects in skein theory and quantum cluster charts
AU  - Jennifer Brown
AU  - Juan Ramón Gómez García
AU  - David Jordan
AU  - Matthias Vancraeynest
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09308
UR  - https://arxiv.org/abs/2609.09308
AB  - We prove a modified invertibility property for the parabolic defects introduced in arXiv:2102.12283, arXiv:2505.14836. Namely, we show that the Borel defect cancels its dual, up to insertion of an invertible Weyl defect and up to restriction to an open-subcategory. The main result holds for an arbitrary reductive group G -- for illustration we give extended computations for G=SL_3. Along the way, we introduce a defect skein theory with defects in both codimension one and two, which is compatible with gluing of defect 3-manifolds and defect surfaces. Our results provide a potential defect skein theoretic construction of certain standard charts which appears frequently in quantum cluster varieties associated to surfaces.
ER  -