PreprintCC BY 4.0arXiv
Calculating double-leaf coefficients in the Hecke category
Abstract
Given a morphism of Abe-Bott-Samelson bimodules, we construct an algorithm for computing its double-leaves coefficients. The key ingredient is a modification of Bruhat upper-triangularity which allows us to use forward substitution to solve for the double-leaf coefficients. We provide a complete implementation of the algorithm in the Sage computer algebra system. We use this to compute the Zamolodchikov 3-color relation in type H3 for balanced realizations. We further simplify the 3-color relation using thick Soergel calculus and express it as a difference of two thick Elias--Williamson diagrams.
Related
- Explicit H3 relation in the diagrammatic Hecke category
- Structure of derived Hecke algebras with coefficients in torsion-free profinite rings
- Double affine Frobenius Hecke algebras
- A bar operation on the double affine Hecke algebra
- Hecke Subalgebras and Local Newforms for the Metaplectic Double Cover of SL2(ℚp)
BibTeX
@misc{sandvik2026calculating,
title = {{Calculating double-leaf coefficients in the Hecke category}},
author = {Colton Sandvik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05299},
eprint = {2610.05299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05299},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Calculating double-leaf coefficients in the Hecke category
AU - Colton Sandvik
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05299
UR - https://arxiv.org/abs/2610.05299
AB - Given a morphism of Abe-Bott-Samelson bimodules, we construct an algorithm for computing its double-leaves coefficients. The key ingredient is a modification of Bruhat upper-triangularity which allows us to use forward substitution to solve for the double-leaf coefficients. We provide a complete implementation of the algorithm in the Sage computer algebra system. We use this to compute the Zamolodchikov 3-color relation in type H_3 for balanced realizations. We further simplify the 3-color relation using thick Soergel calculus and express it as a difference of two thick Elias--Williamson diagrams.
ER -