SPEAKER:     Claus Sorensen

TITLE:    Level-raising for Saito-Kurokawa forms

ABSTRACT:
We begin by giving an adelic interpretation of the classical level-raising theorem due to Ribet. Basically it says that, modulo l, a cuspidal automorphic representation of PGL(2) has a Steinberg component at q if a certain necessary condition is satisfied. Bellaiche and Clozel have proved the analogue for other groups of rank one at q. In this talk we will present a result in higher rank. Concretely, we take G to be an inner form of GSp(4) which is compact at infinity modulo the center. We then prove that, modulo l, an automorphic representation has a generic component at q under some explicit condition. We apply this to Saito-Kurokawa forms, which are known to be locally non-generic everywhere. At the end of the talk, we will discuss some possible refinements and applications of the main result.