Representation Theory

This chapter has two main themes. The first theme concerns the nonsupercuspidal representations of GSp(4) over a non-archimedean local field. These representations were classified by Sally and Tadić and we summarize their work. Using this classification, we find it convenient to list and name all non-supercuspidal representations in the form of the fundamental Table A.1. With this list at hand we consider the conjectural local Langlands correspondence for GSp(4) as regards non-supercuspidal representations. As it happens, the desiderata of the conjectural local Langlands correspondence determine the L-parameters attached to all non-supercuspidal representations, and we describe these L-parameters explicitly.