论文标题
较高替补覆盖组的古典theta升降机
Classical Theta Lifts for Higher Metaplectic Covering Group
论文作者
论文摘要
经典的theta对应关系在特殊正交组上的自动形态表示与符号群体或其双重覆盖率上的自动形态表示之间建立了关系。通过用作由Weil表示构建的符号群的元容器双盖上的积分内核A theta系列来实现此对应关系。还有类似的局部对应关系。在这项工作中，我们介绍了经典的theta对应关系的扩展，以与符号和特殊正交组的更高程度的元容器覆盖。这里的关键问题是，对于更高的覆盖率，没有Weil表示的类似物，需要其他成分。我们的工作反映了一个更广泛的范式：用于代数群体或其双重覆盖的自动形式的建筑通常应扩展到更高程度的跨度覆盖范围。
The classical theta correspondence establishes a relationship between automorphic representations on special orthogonal groups and automorphic representations on symplectic groups or their double covers. This correspondence is achieved by using as integral kernel a theta series on the metaplectic double cover of a symplectic group that is constructed from the Weil representation. There is also an analogous local correspondence. In this work we present an extension of the classical theta correspondence to higher degree metaplectic covers of symplectic and special orthogonal groups. The key issue here is that for higher degree covers there is no analogue of the Weil representation, and additional ingredients are needed. Our work reflects a broader paradigm: constructions in automorphic forms that work for algebraic groups or their double covers should often extend to higher degree metaplectic covers.
