Structure of the module of vector‐valued modular forms

By Christopher Marks, Geoffrey Mason. 2009

46 citations recorded by the source corpus.

Let V be a representation of the modular group Γ of dimension p. We show that the ℤ‐graded space ℋ(V) of holomorphic vector‐valued modular forms associated to V is a free module of rank p over the algebra ℳ of classical holomorphic modular forms. We study the nature of ℋ considered as a functor from Γ‐modules to graded ℳ‐lattices and give some applications, including the calculation of the Hilbert–Poincaré series of ℋ(V) in some cases.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/951ee9072910ae19ba6dbbd8ebc21c84c55c8877

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In Geometry and Topology

1. C. Franc
2. Geoffrey Mason
3. F. Pellarin
4. Siu-Hung Ng

In Mathematical Physics

1. C. Franc
2. Geoffrey Mason
3. F. Pellarin
4. Siu-Hung Ng

Citations in the corpus

• Hypergeometric series, modular linear differential equations and vector-valued modular forms (2015, background): “Subtleties arise in this case because ρ is indecomposable and not irreducible ([35], [33]).”