All (3,0) admissible solutions are expressed via a universal _3F_2 hypergeometric formula; (3,3) solutions are built from them using Bantay-Gannon duality with only 7 of 15 having proper fusion rules, and further (3,6) and (3,9) solutions are generated as integer points on a polytope via quasi-char
Gannon,The theory of vector-modular forms for the modular group,Contrib
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We explain the basic ideas, describe with proofs the main results, and demonstrate the effectiveness, of an evolving theory of vector-valued modular forms (vvmf). To keep the exposition concrete, we restrict here to the special case of the modular group. Among other things,we construct vvmf for arbitrary multipliers, solve the Mittag-Leffler problem here, establish Serre duality and find a dimension formula for holomorphic vvmf, all in far greater generality than has been done elsewhere. More important, the new ideas involved are sufficiently simple and robust that this entire theory extends directly to any genus-0 Fuchsian group.
fields
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UNVERDICTED 2representative citing papers
Admissible solutions to MLDEs with ≤6 characters and c_eff ≤24 are enumerated; tenable ones with good fusion rules are identified, with some linked to specific CFTs and MTC classes.
citing papers explorer
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Quasi-Characters for three-character Rational Conformal Field Theories
All (3,0) admissible solutions are expressed via a universal _3F_2 hypergeometric formula; (3,3) solutions are built from them using Bantay-Gannon duality with only 7 of 15 having proper fusion rules, and further (3,6) and (3,9) solutions are generated as integer points on a polytope via quasi-char
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Updating the holomorphic modular bootstrap
Admissible solutions to MLDEs with ≤6 characters and c_eff ≤24 are enumerated; tenable ones with good fusion rules are identified, with some linked to specific CFTs and MTC classes.