对称破缺算子的F方法
F-method for symmetry breaking operators
摘要：
我们提供了一些见解，在研究的分支问题的约化群，和一种方法的调查对称性破缺运营商。首先，我们给出了介于约化李群及其约化子群的两个诱导表示之间的线性无关连续（微分）算子有限性的几何判据。其次，我们将局部算子的F-方法推广到非局部算子。然后，我们通过共形几何中的具体例子来说明这一思想，并解释F-方法如何用于对称性破缺算子的详细分析，例如，寻找正则对称破缺算子的函数方程和显式留数公式。
英文摘要：
We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators. First, we give geometric criteria for finiteness property of linearly independent continuous (respectively, differential) operators that intertwine two induced representations of reductive Lie groups and their reductive subgroups. Second, we extend the F-method known for local operators to non-local operators. We then illustrate the idea by concrete examples in conformal geometry, and explain how the F-method works for detailed analysis of symmetry breaking operators, e.g., finding functional equations and explicit residue formulae of regular symmetry breaking operators with meromorphic parameters.
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