Unitary Jacobi forms and primitive theta functions

确定了指数为极大偶整矩阵的Jacobi Hecke代数的结构，得到了对应于该代数不可约表示的带状球函数，并证明了非交换Jacobi Hecke代数与二面体群的群环之间的关系（与N. Hashizhibi）。作为一个整体问题，我们利用θ提升和Klingen Eisenstein级数（与Y. Iwahori）。

We determined the structure of Jacobi Hecke algebra whose index is a maximal even integral matrix and obtained zonal spherical functions corresponding to irreducible representations of the Hecke algebra, moreover, we showed a relation between a non-commutative Jacobi Hecke algebra and the group ring of a dihedral group (joint work with N. Hashizume). As a global problem, we gave a new system of generators for the ring of paramodular forms of degree 2 and level 2 or 3, by using theta lifts and Klingen Eisenstein series (joint work with Y. Iwahori).