正则对称破缺算子的留数公式
Residue formula for regular symmetry breaking operators
摘要：
证明了共形协变积分算子在${\bf R}^n$及其超平面上的亚纯延拓的一个显式留数公式。这些结果提供了球面上微分形式与其全测地超曲面上微分形式之间的共形协变微分对称破缺算子的简单而新的构造，这些微分对称破缺算子在[Kobayashi-Kubo-Pevzner，Lect. Notes Math.（2016）]中引入。此外，我们确定了$O(n+1,1)$和$O(n,1)$的主列表示之间的矩阵值正则对称破缺算子的零点。
英文摘要：
We prove an explicit residue formula for a meromorphic continuation of conformally covariant integral operators between differential forms on ${\bf R}^n$ and on its hyperplane. The results provide a simple and new construction of the conformally covariant differential symmetry breaking operators between differential forms on the sphere and those on its totally geodesic hypersurface that were introduced in [Kobayashi-Kubo-Pevzner, Lect. Notes Math. (2016)]. Moreover, we determine the zeros of the matrix-valued regular symmetry breaking operators between principal series representations of $O(n+1,1)$ and $O(n,1)$.
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