math.QA — Quantum Algebra

A Uniform Calculation of Weight-Preserving Infinitesimal Braid Deformations in Type D

Contributed by Hangang Wang

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 integrable family belongs to earlier multiparameter constructions; an exact parameter dictionary is provided. No bibliographic priority claim is made for the full tangent-space exhaustion. The proof is uniform in $n$; finite-rank computations are diagnostics.