地方和全球Maass关系（扩大版）
Local and global Maass relations (expanded version)
摘要：
我们刻画了GSp（4，F）（其中F是p-adic域）的不可约的、可容许的球面表示，这些表示出现在特定的CAP表示中，在一个特殊的Bessel模型中，它们的球面向量所满足的关系.这些局部关系是类似的马斯关系满足的傅里叶系数的西格尔模形式的程度2的图像中的Saito-Kurokawa提升。我们展示了如何经典的马斯关系可以推导出从局部关系的表示论的方式，而不求助于建设斋藤-黑川升降机的傅里叶系数的半整权模形式或雅可比形式。作为我们方法的一个额外应用，我们给出了涉及特定傅里叶系数平均值的斋藤-黑川提升的新特征。
英文摘要：
We characterize the irreducible, admissible, spherical representations of GSp(4,F) (where F is a p-adic field) that occur in certain CAP representations in terms of relations satisfied by their spherical vector in a special Bessel model. These local relations are analogous to the Maass relations satisfied by the Fourier coefficients of Siegel modular forms of degree 2 in the image of the Saito-Kurokawa lifting. We show how the classical Maass relations can be deduced from the local relations in a representation theoretic way, without recourse to the construction of Saito-Kurokawa lifts in terms of Fourier coefficients of half-integral weight modular forms or Jacobi forms. As an additional application of our methods, we give a new characterization of Saito-Kurokawa lifts involving a certain average of Fourier coefficients.
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