Howe's Rank and Dual Pair Correspondence in Semistable Range

In this book we study representations of classical Lie groups based on the analysis on Euclidean spaces. Classical groups come in pairs known as the dual reductive pairs. The main theme of this book is to develope the ideas initiated by A. Weil R. Howe and others concerning the oscillator representation and dual pair correspondence. The results from this book can be used to construct unipotent representations and study the branching laws.