Elementary Etudes on a Special Representation of the (Real) Symplectic Group and211 the Maass Lift

摘要

The report starts by fixing the notations for Siegel and Jacobi forms. It211u001edescribes the Mass lift in the version of Eichler and Zagier, transfers 211u001eeverything to a 'semiclassical' setting by looking at forms as functions on the 211u001egroup. Representations are introduced as lowest weight representations defined by 211u001ethe holomorphic forms being their vacuum vectors. Then the main part of these 211u001enotes consist in the analysis of the infinitesimal representations as 211u001erepresentations of the (compexified) symplectic and Jacobi Lie algebras, hoping 211u001eto find here some interest not only for the automorphic theory. While 211u001econcentrating on the treatment of the holomorphic case, the setting is meant to 211u001eprepare a similar treatment of more general forms and to set a base to an adelic 211u001etreatment.