Degenerate principal series of metaplectic groups and Howe correspondence

Abstract

The main purpose of this article is to supplement the authors' results on degenerate principal series representations of real symplectic groups with the analogous results for metaplectic groups. The basic theme, as in the previous case, is that their structures are anticipated by certain natural subrepresentations constructed from Howe correspondence. This supplement is necessary as these representations play a key role in understanding the basic structure of Howe correspondence (and its complications in the archimedean case), and their global counterparts play an equally essential part in the proof of Siegel-Weil formula and its generalizations (work of Kudla-Rallis). The full results in the metaplectic case also shed light on the seeming peculiarities, when the results in the symplectic case are viewed in their isolation.