Skew-holomorphic Jacobi forms of index 1 and Siegel modular forms of half-integral weight (Q1434320)

It is well known that Kohnen's ``\(+\)''-space of elliptic modular forms of half-integral weights \(k-1/2\) is isomorphic to the space of holomorphic resp. skew-holomorphic Jacobi forms of index 1 whenenver \(k\) is even resp. odd. In this paper the author generalizes this result to higher degrees. The space of skew-holomorphic Jacobi forms of odd resp. even weight \(k\) index 1 and degree \(n\) is isomorphic to a certain subspace of Siegel modular forms of degree \(n\) and weight \(k- 1/2\) without resp. with character. This subspace is a generalization of Kohnen's ``\(+\)''-space. Moreover, the isomorphism is shown to commute with Hecke operators.