A certain relation between Jacobi forms of half integral weights and Siegel modular forms of integral weight (Q5956166)

In an earlier paper \textit{T. Ibukiyama} [Comment. Math. Univ. St. Pauli 41, 109-124 (1992; Zbl 0787.11015)] described a relation between the space of Jacobi forms of degree \(n\), integral weight \(k\) and index 1 on \(H_n\times \mathbb{C}^n\) and the space of Siegel modular forms of half-integral weight \(k-1/2\) with respect to \(\Gamma_{n,0}(4)\) preserving the action of Hecke operators. In the paper under review the author derives an analogous result for Jacobi forms of weight \(k+1/2\) and Siegel modular forms of weight \(k\).