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Jacobi forms can be considered as vector valued modular forms, and Jacobi forms of critical weight correspond to vector valued modular forms of weight $\frac12$.
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Ibukiyama, T. and Skoruppa, N-P., On Jacobi and Siegel modular forms of weight 1. Appendix to Cris Poor and David Yuen, Dimensions of cusp forms for Γ 0 ( p ) \Gamma_{0}(p) in degree two and small weights, to appear
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Ibukiyama, T. and Skoruppa, N-P., Siegel and Orthogonal Modular Forms of Critical Weight, in preparation
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Skoruppa N-P., On Weil Representations Associated to Finite Quadratic Modules, in preparation
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