Siegel modular forms and finite symplectic groups

2008/04/23 by Francesco Dalla Piazza, Bert van Geemen, Piazza, Francesco Dalla +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.0804.3769

Minor changes. Written in ATMP format

arxiv created 2008/05/05 · arxiv updated 2009/12/01

Abstract

The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this representation, for various (small) values of the genus and the level, into irreducible representations. As a consequence we obtain uniqueness results for certain modular forms related to the superstring measure, a better understanding of certain modular forms in genus three studied by D'Hoker and Phong as well as a new construction of Miyawaki's cusp form of weight twelve in genus three.

Cited by

• RNS superstring measure for genus 3

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