分野別セミナー

As a generalization of the Saito-Kurokawa lifting to the
higher genus, Ikeda constructed a Langlands functorial lifting of
elliptic modular forms to Siegel modular forms (i.e. automorphic forms
on the symplectic group) of arbitrary even genus, which is so-called the
Duke-Imamoglu (or Ikeda) lifting. On the other hand, Hida and Coleman
constructed the $p$-adic families of elliptic modular forms of finite
slope, varying continuously $p$-adically the weight and the Nebentypus
characters, which could be interpolated by some "$\Lambda$-adic" modular
forms. In this context, starting from the $p$-adic families of elliptic
modular forms, we'd show you how to construct certain p-adic families of
Siegel modular forms of even genus by means of an analogy of Ikeda's
lifting process. Moreover, as an application, we'd also like to propose
a generalized Duke-Imamoglu lifting to be adaptable to some elliptic
modular forms of $p$-power level, and also to some automorphic
representations of PGL(2) over any totally real field.