The Saito–Kurokawa space of PGSp4 and its transfer to inner forms

Abstract

We discuss the construction, characterization and classification of the Saito–Kurokawa representations of PGSp4 and its inner forms, interpreting them in the framework of Arthur’s conjectures. These Saito–Kurokawa representations are among the first examples of the so-called CAP representations or shadows of Eisenstein series.