On some free algebras of orthogonal modular forms

Abstract

For 25 orthogonal groups of signature $(2,n)$ related to the root lattices $A_1$, $2A_1$, $3A_1$, $4A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $A_6$, $A_7$, $D_4$, $D_5$, $D_6$, $D_7$, $D_8$, $E_6$, $E_7$, we prove that the algebras of modular forms on symmetric domains of type IV are freely generated by the additive lifts of some special Jacobi forms. The proof is universal and elementary.

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References in corpus (1)

• The D_8-tower of weak Jacobi forms and applications

Cited by in corpus (7)

• The classification of free algebras of orthogonal modular forms
• Congruence Subgroups and Orthogonal Groups
• Projective spaces as orthogonal modular varieties
• Simple lattices and free algebras of modular forms
• Free algebras of modular forms on ball quotients
• Maximal Discrete Subgroups of $S{O}^{+}(2,n+2)$
• K3 Surfaces and Orthogonal Modular Forms