Résume | The conservation relation of the theta correspondence, which was proved
by Sun-Zhu, gives useful bounds on the first occurrence of non-vanishing
theta-lifts. In this talk, we will present a new proof by answering a
conjecture of Kudla and Rallis on the multiplicity of certain
irreducible quotients of degenerate principle series of symplectic
groups. This is achieved mainly by studying the Jacquet-modules of the
global sections of a line bundle on a symplectic Grassmannian. |