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arXiv · 2610.05299

Calculating double-leaf coefficients in the Hecke category

Colton Sandvik
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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 $H_3$ 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.

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Colton Sandvik. 2026-10-04. Calculating double-leaf coefficients in the Hecke category. https://arxiv.org/abs/2610.05299

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