We undertake a detailed study of the lowest weight modules for Hermitian symmetric pair (G,K), where G= Sp4(R) and K is its maximal compact subgroup. In particular, we determine K-types composition series, write down explicit differential operators that navigate all highest vectors such module starting from unique vector. By rewriting these in classical language, show automorphic forms on G cor...

In this paper we study the pullback of a Siegel Eisenstein series on Sp2m+2n to Sp2m×Sp2n. There is a well-established literature on such pullbacks. In the case that m = n Garrett showed that the pullback is actually a cusp form in each variable separately. Here we generalize this result showing the pullback is cuspidal in the smaller variable in the case m 6= n. Such results have applications ...

2009 Introduction In the following we describe some examples of Calabi-Yau manifolds that arise as desingularizations of certain Siegel threefolds. Here by a Calabi-Yau mani-fold we understand a smooth complex projective variety which admits a holo-morphic differential form of degree three without zeros and such that the first Betti number is zero. This differential form is unique up to a const...