Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular forms, deformation of punctured spheres, and extensions of
  symmetric tensor representations   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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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th