Eisenstein metrics

We study families of metrics on automorphic vector bundles associated with representations of the modular group. These metrics are defined using an Eisenstein series construction. We show that in certain cases, the residue of these Eisenstein metrics at their rightmost pole is a harmonic metric for...

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Bibliographic Details
Published in:Canadian journal of mathematics 2023-06, Vol.75 (3), p.778-803
Main Author: Franc, Cameron
Format: Article
Language:English
Subjects:
Correspondence
Modular construction
Partial differential equations
Representations
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Summary:We study families of metrics on automorphic vector bundles associated with representations of the modular group. These metrics are defined using an Eisenstein series construction. We show that in certain cases, the residue of these Eisenstein metrics at their rightmost pole is a harmonic metric for the underlying representation of the modular group. The last section of the paper considers the case of a family of representations that are indecomposable but not irreducible. The analysis of the corresponding Eisenstein metrics, and the location of their rightmost pole, is an open question whose resolution depends on the asymptotics of matrix-valued Kloosterman sums.
ISSN:0008-414X
1496-4279
DOI:10.4153/S0008414X21000626