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.