Illinois Journal of Mathematics

Irreducible vector-valued modular forms of dimension less than six

Christopher Marks

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Abstract

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, $T$-unitarizable representations of the full modular group, of dimension less than six. For representations of dimension less than four, it is shown that the associated space of vector-valued modular forms is a cyclic module over a certain skew polynomial ring of differential operators. For dimensions four and five, a complete list of possible Hilbert–Poincaré series is given, using the fact that the space of vector-valued modular forms is a free module over the ring of classical modular forms for the full modular group. A mild restriction is then placed on the class of representation considered in these dimensions, and this again yields an explicit determination of the associated Hilbert–Poincaré series.

Article information

Source
Illinois J. Math., Volume 55, Number 4 (2011), 1267-1297.

Dates
First available in Project Euclid: 12 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1373636684

Digital Object Identifier
doi:10.1215/ijm/1373636684

Mathematical Reviews number (MathSciNet)
MR3082869

Zentralblatt MATH identifier
1343.11052

Subjects
Primary: 11F03: Modular and automorphic functions 11F99: None of the above, but in this section

Citation

Marks, Christopher. Irreducible vector-valued modular forms of dimension less than six. Illinois J. Math. 55 (2011), no. 4, 1267--1297. doi:10.1215/ijm/1373636684. https://projecteuclid.org/euclid.ijm/1373636684


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