Kudla-Millson形式通过Mathai-Quillen形式主义

IF 0.6 3区数学 Q3 MATHEMATICS Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2023-10-05 DOI:10.4153/s0008414x23000573

Romain Branchereau

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引用次数: 1

摘要

Kudla和Millson的提升理论的一个重要组成部分是利用Howe的微分算子在正交对称空间上构造$q$ -形式$\varphi_{KM}$。这种形式可以看作是实方向矢量束的Thom形式。我们证明Kudla-Millson形式可以从Mathai和Quillen的正则构造中恢复。Garcia在对称空间为厄米时，对签名$(2,q)$也得到了类似的结果，并将其推广到任意签名。

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The Kudla-Millson form via the Mathai-Quillen formalism

Abstract A crucial ingredient in the theory of theta liftings of Kudla and Millson is the construction of a $q$ -form $\varphi_{KM}$ on an orthogonal symmetric space, using Howe's differential operators. This form can be seen as a Thom form of a real oriented vector bundle. We show that the Kudla-Millson form can be recovered from a canonical construction of Mathai and Quillen. A similar result was obtaind by Garcia for signature $(2,q)$ in case the symmetric space is hermitian and we extend it to arbitrary signature.

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来源期刊

Canadian Journal of Mathematics-Journal Canadien De Mathematiques 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4.5 months

期刊介绍： The Canadian Journal of Mathematics (CJM) publishes original, high-quality research papers in all branches of mathematics. The Journal is a flagship publication of the Canadian Mathematical Society and has been published continuously since 1949. New research papers are published continuously online and collated into print issues six times each year. To be submitted to the Journal, papers should be at least 18 pages long and may be written in English or in French. Shorter papers should be submitted to the Canadian Mathematical Bulletin. Le Journal canadien de mathématiques (JCM) publie des articles de recherche innovants de grande qualité dans toutes les branches des mathématiques. Publication phare de la Société mathématique du Canada, il est publié en continu depuis 1949. En ligne, la revue propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés six fois par année. Les textes présentés au JCM doivent compter au moins 18 pages et être rédigés en anglais ou en français. C’est le Bulletin canadien de mathématiques qui reçoit les articles plus courts.