Sturm's operator acting on vector valued K‐types

Abstract

We define Sturm's operator for vector valued Siegel modular forms obtaining an explicit description of their holomorphic projection in case of large absolute weight.However, for small absolute weight, Sturm's operator produces phantom terms in addition. This confirms our earlier results for scalar Siegel modular forms. K E Y W O R D Sholomorphic projection, integral operator, Siegel modular forms, sturm operator M S C ( 2 0 1 0 ) 11F30, 11F46This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.