调制群
Modulation groups
AI总结：
本文提出调制群的概念，将其与Schwartz空间的表示联系起来，并探讨其与代数群及Poisson求和猜想的关系。
摘要：
Braverman和Kazhdan的猜想，以及Ngö和Sakellaridis的猜想，推动了某些球面变种的Schwartz空间的发展。我们证明，在适当假设下，这些Schwartz空间自然地成为一个称为调制群的群的表示。这为metaplectic群的定义表示提供了广泛的推广。详细讨论了向量空间和偶数变量下的二次锥零 locus 的例子。在这两种情况下，调制群与代数群密切相关，我们提出了一种将调制群与ind-代数群联系起来的猜想性方法。最后，我们讨论了adelization以及调制群表示与Poisson求和猜想之间的关系。
英文摘要：
Conjectures of Braverman and Kazhdan, Ngô and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptions these Schwartz spaces are naturally a representation of a group that we christen the modulation group. This provides a broad generalization of the defining representation of the metaplectic group. The example of a vector space and the zero locus of a quadric cone in an even number of variables are discussed in detail. In both of these cases the modulation group is closely related to algebraic groups, and we propose a conjectural method of linking modulation groups to ind-algebraic groups in general. At the end of the paper we discuss adelization and the relationship between representations of modulation groups and the Poisson summation conjecture.
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