The Kudla-Millson form via the Mathai-Quillen formalism
Abstract
In km2, Kudla and Millson constructed a q-form 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 mq Mathai and Quillen constructed a 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.
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