Open Access
December 2009 Siegel modular forms and finite symplectic groups
Francesco Dalla Piazza, Bert van Geemen
Adv. Theor. Math. Phys. 13(6): 1771-1814 (December 2009).


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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Francesco Dalla Piazza. Bert van Geemen. "Siegel modular forms and finite symplectic groups." Adv. Theor. Math. Phys. 13 (6) 1771 - 1814, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2010

zbMATH: 1200.81091
MathSciNet: MR2678996

Rights: Copyright © 2009 International Press of Boston

Vol.13 • No. 6 • December 2009
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