On Siegel modular forms of half-integral weights and Jacobi forms

@article{Takase1999OnSM,
  title={On Siegel modular forms of half-integral weights and Jacobi forms},
  author={Koichi Y. Takase},
  journal={Transactions of the American Mathematical Society},
  year={1999},
  volume={351},
  pages={735-780}
}
  • K. Takase
  • Published 1999
  • Mathematics
  • Transactions of the American Mathematical Society
We will establish a bijective correspondence between the space of the cuspidal Jacobi forms and the space of the half-integral weight Siegel cusp forms which is compatible with the action of the Hecke operators. This correspondence is based on a bijective correspondence between the irreducible unitary representations of a two-fold covering group of a symplectic group and a Jacobi group (that is, a semidirect product of a symplectic group and a Heisenberg group). The classical results due to… 
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