发表机构
Beijing Institute of Mathematical Sciences and Applications (BIMSA); Yau Mathematical Sciences Center (YMSC), Tsinghua University; Faculty of Mathematics, National Research University Higher School of Economics（北京国际数学研究中心; 清华大学丘成桐数学科学中心; 俄罗斯国立高等经济学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究六族可积自旋-1/2链的Jordan结构与动力学极限，揭示幂零演化与谱缺陷的联系，并给出保守侵蚀的精确振幅及排除保守马尔可夫实现的标准。
AI 中文摘要
我们研究了通过boost自同构方法得到的六族可积自旋-1/2链中的Jordan结构与动力学极限。局部算子代数将有限周期链上的幂零演化与谱可加性中的中心缺陷、多项式酉R矩阵及常数辫极限联系起来。对于保守端点侵蚀，我们确定了特征多项式与最小多项式，并表明Jordan划分可以改变而这两个多项式保持不变。我们还识别了删除极限，这些极限区分了第5类中通过对角相似性移除符号的奇偶性障碍与第6类中的奇偶性幂零依赖性。匹配展开与碎裂递推给出了具有杀伤过程的精确振幅与存活概率。此外，我们建立了排除保守马尔可夫实现的标准，并确定了哪些指定反应密度的保守完备化允许差分形式的正则R矩阵。
英文摘要
We investigate Jordan structure and dynamical limits in six families of integrable spin-$\frac{1}{2}$ chains obtained from the boost automorphism method. Local operator algebras connect nilpotent evolution on finite periodic chains to central defects in spectral additivity, polynomial unipotent $R$-matrices and constant braid limits. For conservative endpoint erosion, we determine the characteristic and minimal polynomials and show that the Jordan partition can change while both polynomials remain unchanged. We also identify the deletion limits that distinguish the parity obstruction to removing signs by diagonal similarity in Class 5 from the parity nilpotent dependence in Class 6. Matching expansions and fragmentation recursions yield exact amplitudes and survival probabilities for processes with killing. In addition, we establish criteria excluding conservative Markov realizations and determine which conservative completions of specified reaction densities admit regular $R$-matrices of difference form.
