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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

The Kudla-Millson form via the Mathai-Quillen formalism

Résumé

Kudla and Millson constructed a $q$-form $\varphi_{KM}$ 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 Garcia for signature $(2,q)$ in case the symmetric space is hermitian and we extend it to an arbitrary signature.

Dates et versions

hal-04001212 , version 1 (22-02-2023)

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Romain Branchereau. The Kudla-Millson form via the Mathai-Quillen formalism. 2022. ⟨hal-04001212⟩
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