论文标题
通过Mathai-Quillen形式主义的Kudla-Millson表格
The Kudla-Millson form via the Mathai-Quillen formalism
论文作者
论文摘要
在\ cite {km2}中，Kudla和Millson使用Howe的差分运算符在正交对称空间上构建了一个$ q $ - form $φ_{km} $。它是其theta提升理论中的重要成分。该形式可以看作是实际取向矢量束的汤姆形式。在\ cite {mq} Mathai和Quillen构建了{\ em canonical} thom形式，我们展示了如何通过其结构来恢复Kudla-Millson形式。如果对称空间为Hermitian，并且我们将其扩展到任意签名，则由\ cite {garcia}获得类似的结果。
In \cite{km2}, Kudla and Millson constructed a $q$-form $φ_{KM}$ on an orthogonal symmetric space using Howe's differential operators. It is a crucial ingredient in their theory of theta lifting. This form can be seen as a Thom form of a real oriented vector bundle. In \cite{mq} Mathai and Quillen constructed a {\em canonical} Thom form and we show how to recover the Kudla-Millson form via their construction. A similar result was obtained by \cite{garcia} for signature $(2,q)$ in case the symmetric space is hermitian and we extend it to an arbitrary signature.
