Weight Changing Operators for Automorphic Forms on Grassmannians and   Differential Properties of Certain Theta Lifts
  We define weight changing operators for automorphic forms on Grassmannians, i.e., on orthogonal groups, and investigate their basic properties. We then evaluate their action on theta kernels, and prove that theta lifts of modular forms, in which the theta kernel involves polynomials of a special type, have some interesting differential properties. 
Shaul Zemel
math.NT