In [S. S. Kudla and J. J. Millson, Publ. Math., Inst. Hautes Étud. Sci. 71, 121–172 (1990; Zbl 0722.11026)] liftings are constructed from the cohomology with compact supports of locally symmetric spaces associated to the quadratic group \(\mathrm{O}(p, q)\) to the classical holomorphic Siegel modular forms of weight \((p+ q)/2\).
In the present paper this technique, based on theta series attached to the Weil representation of the dual pair \((\mathrm{O}(p, q),\widetilde{\mathrm{Sp}}(n))\), is generalized to the case of cohomology with certain local coefficients. The coefficient bundles considered are flat bundles arising from harmonic tensors. As a result of this lifting process, the authors obtain new vector-valued Siegel modular forms.