On some free algebras of orthogonal modular forms II

TL;DR

This paper constructs 16 free algebras of orthogonal modular forms on symmetric domains of type IV for specific reflection groups, establishing their structure and proving the modularity of associated Fourier-Jacobi expansions.

Contribution

It introduces new free algebras of modular forms for certain reflection groups and proves the modularity of their Fourier-Jacobi expansions.

Findings

Constructed 16 free algebras of modular forms.

Proved modularity of formal Fourier-Jacobi expansions.

Linked algebraic structures to specific reflection groups.

Abstract

In this paper we construct 16 free algebras of modular forms on symmetric domains of type IV for some reflection groups related to the eight lattices $A_1(2)$, $A_1(3)$, $A_1(4)$, $2A_1(2)$, $A_2(2)$, $A_2(3)$, $A_3(2)$, $D_4(2)$. As a corollary, we prove the modularity of formal Fourier--Jacobi expansions for these reflection groups.