We give an explicit theory of differential operators
acting on Siegel modular forms which preserves automorphy
under the restriction to any diagonal blocks of any size.
For example, we give a generating function including all such operators.
We also show that the Taylor expansion of Siegel modular forms
(or Jacobi forms) w.r.t. off-diagonal-blocks elements
can be recovered by the images of differential operators.
These operators are important in various points, including the calculation
of special values of L functions, or liftings of automorphic forms.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246