Abstract
In this paper we construct 16 free algebras of modular forms on type IV symmetric domains for some reflection groups related to the eight rescaled root 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.
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