{"id":"hexagon/2610.00581","pdf":"https://hexagonmath.org/pdf/2610.00581v1","url":"https://hexagonmath.org/abs/2610.00581v1","tags":["math.RT","msc:16T25","msc:17B37","Yang–Baxter equation","exact computation","formal deformations","infinitesimal braid deformations","quantum groups","type D"],"score":0,"title":"A Uniform Calculation of Weight-Preserving Infinitesimal Braid Deformations in Type D","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Hangang Wang"],"reviews":0,"subject":"math.QA","summary":"Over $\\mathbb Q(q)$, for every $n\\ge4$, we calculate the full space of classical-weight-preserving solutions of the linearized braid equation at the standard type-$D_n$ vector braiding. Its dimension is $(n+1)(n+2)/2$. A coordinate slice for scalar and parameter variations, diagonal vector-basis changes, and alternating twists reduces the upper bound to a homogeneous vanishing problem. Outer-pair coefficients eliminate the zero-weight block through a recurrence closed by the two central weights. We also give a functorial formal local parametrization over local Artin algebras. The explicit…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex","Python","SymPy","MATLAB"],"discussed":0,"published":"2026-10-27","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}