Advances in Theoretical and Mathematical Physics

Siegel modular forms and finite symplectic groups

Francesco Dalla Piazza and Bert van Geemen

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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.

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Adv. Theor. Math. Phys., Volume 13, Number 6 (2009), 1771-1814.

First available in Project Euclid: 17 August 2010

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Dalla Piazza, Francesco; van Geemen, Bert. Siegel modular forms and finite symplectic groups. Adv. Theor. Math. Phys. 13 (2009), no. 6, 1771--1814.

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