Representations of Nilpotent Lie Groups and Their Applications

There has been no exposition of group representations and harmonic analysis suitable for graduate students for over twenty years. In this the first of two projected volumes the authors remedy the situation by surveying all the basic theory developed since the pioneering work of Kirillov in 1958 and consolidating more recent results. Topics covered include basic Kirillov theory algorithms for parametrizing all coadjoint orbits. The authors have not only given here a modern account of all topics necessary for current research but have also included many computed examples. This volume can serve then either as a handbook for specialists with a complete self-contained exposition of major results or as a textbook suitable for graduate courses in harmonic analysis.