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arXiv · 2004.04716

Modular forms, deformation of punctured spheres, and extensions of symmetric tensor representations

Gabriele Bogo
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Abstract

Let~$X=\Po/\Gamma$ be an~$n$-punctured sphere, $n>3$. We introduce and study~$n-3$ deformation operators on the space of modular forms~$M_*(\Gamma)$ based on the classical theory of uniformizing differential equations and accessory parameters. When restricting to modular functions, we recover a construction in Teichm\"uller theory related to the deformation of the complex structure of~$X$. We describe the deformation operators in terms of derivations with respect to Eichler integrals of weight-four cusp forms, and in terms of vector-valued modular forms attached to extensions of symmetric tensor representations.

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Gabriele Bogo. 2020-04-09. Modular forms, deformation of punctured spheres, and extensions of symmetric tensor representations. https://arxiv.org/abs/2004.04716

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