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PreprintarXiv licencearXiv

Explicit H3 relation in the diagrammatic Hecke category

  • Lev Nechitailo
Open at sourcePDFDOICite

Abstract

We compute the missing three-color relation in type H3 as an explicit R-linear combination of double leaves. The expression has 43 424 nonzero polynomial coefficients with scalars in ℤ[φ], where φ= (1 + √5)/2. We verify the relation using exact arithmetic in the computer algebra system GAP. This completes the diagrammatic presentation of the Hecke category of Elias and Williamson.

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Cite

BibTeXRIS
BibTeX
@misc{nechitailo2026explicit,
  title = {{Explicit $H_3$ relation in the diagrammatic Hecke category}},
  author = {Lev Nechitailo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34053},
  eprint = {2609.34053},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34053},
}
RIS
TY  - UNPB
TI  - Explicit H_3 relation in the diagrammatic Hecke category
AU  - Lev Nechitailo
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34053
UR  - https://arxiv.org/abs/2609.34053
AB  - We compute the missing three-color relation in type H_3 as an explicit R-linear combination of double leaves. The expression has 43 424 nonzero polynomial coefficients with scalars in ℤ[φ], where φ= (1 + √5)/2. We verify the relation using exact arithmetic in the computer algebra system GAP. This completes the diagrammatic presentation of the Hecke category of Elias and Williamson.
ER  -