Geodesic
The Kudla–Millson form via the Mathai–Quillen formalism
Canadian journal of mathematics, Tome 76 (2024) no. 5, pp. 1638-1663

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DOI

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.
DOI : 10.4153/S0008414X23000573
Mots-clés : Kudla–Millson form, Mathai–Quillen form, Chern–Weil theory, theta correspondence 
Branchereau, Romain. The Kudla–Millson form via the Mathai–Quillen formalism. Canadian journal of mathematics, Tome 76 (2024) no. 5, pp. 1638-1663. doi: 10.4153/S0008414X23000573
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     title = {The {Kudla{\textendash}Millson} form via the {Mathai{\textendash}Quillen} formalism},
     journal = {Canadian journal of mathematics},
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