发表机构
National Taiwan University; National Central University; Nankai University; Institute of Mathematics `Simion Stoilow', Romanian Academy（台湾大学; 中央大学; 南开大学; 罗马尼亚科学院西奥多·斯托伊洛数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在严格伪凸且全局CR可嵌入的约化条件下，CR Guillemin-Sternberg映射为有界同构，通过消去Fredholm缺陷实现量化与约化的可交换性。
AI 中文摘要
我们证明了CR函数的典范量化-约化可交换定理。在Hsiao-Ma-Marinescu的几何假设下，若零矩水平非空且严格伪凸约化在实维数至少为三时全局CR可嵌入，则CR Guillemin-Sternberg映射在每个实Sobolev阶上都是有界同构。核心新步骤是对其有限维Fredholm缺陷的代数与复解析消去：可乘性消除核，而光滑值域的导子、整依赖及全纯可去性产生全局提升。导子非零性由约化的Szegő奇异性得出；我们也用全局CR峰函数证明了这一点。该映射是Fréchet代数的同构，约化是连通的，且对在零水平附近正的全纯线丛，相应的映射在每个非负张量次数上都是同构。不变全纯截面在每个负次数上消失；当约化基具有正复维数时，截面映射在每个整数次数上都是同构。
英文摘要
We prove a canonical quantization-commutes-with-reduction theorem for CR functions. Under the geometric hypotheses of Hsiao--Ma--Marinescu, if the zero moment level is nonempty and the strictly pseudoconvex reduction is globally CR embeddable of real dimension at least three, the CR Guillemin--Sternberg map is a bounded isomorphism at every real Sobolev order. The central new step is an algebraic and complex-analytic elimination of its finite-dimensional Fredholm defect: multiplicativity removes the kernel, while the conductor of the smooth range, integral dependence, and holomorphic removability produce global lifts. Conductor nonvanishing follows from the reduced Szegő singularity; we also prove it using global CR peak functions. The map is an isomorphism of Fréchet algebras, the reduction is connected, and the corresponding maps for holomorphic line bundles positive near the zero level are isomorphisms in every nonnegative tensor degree. Invariant holomorphic sections vanish in every negative degree; when the reduced base has positive complex dimension, the section maps are isomorphisms in every integer degree.
Comments27 pages
