Square-integrability of metaplectic wave-packet representations onL2(R)

This paper presents a systematic study for harmonic analysis of metaplectic wave-packets in L2(R) via group representation theory. The abstract notions of metaplectic wave-packet groups and metaplectic wave-packet representations will be presented and as the main result, we prove an admissibility condition on closed subgroups of the special linear group SL(2,R), which guarantees square integrability of the associated metaplectic wave-packet representation on L2(R). Finally, we present an analytic study of metaplectic wave-packet representations over admissible subgroups of SL(2,R).