Garrettʹs pullback formula for vector valued Siegel modular forms Original Research Article

Let image be the Siegel Eisenstein series of degree n and weight k. Garrett showed a formula of image on image, where image is the Siegel upper half space of degree n. This formula was useful for investigating the Fourier coefficients of the Klingen Eisenstein series and the algebraicity of the space of Siegel modular forms and of special values of the standard L-functions. We would like to generalize this formula in the case of vector valued Siegel modular forms. In this paper, using a differential operator image by Ibukiyama which sends a scalar valued Siegel modular form to the tensor product of two vector valued Siegel modular forms, under a certain condition, we give a formula of image and investigate the Fourier coefficients of the Klingen Eisenstein series.