  In this paper, we define the concept of Jacobi forms of half-integral weight
using Takase's automorohic factor of weight 1/2 for a two-fold covering group
of the symplectic group on the Siegel upper half plane and find covariant maps
for the Schroedinger-Weil representation. Using these covariant maps, we
construct Jacobi forms of half-integral weight with respect to an arithmetic
subgroup of the Jacobi group.
