Combining presentation of new results with in-depth surveys of recent work, this book focuses on representation theory and harmonic analysis on real and \(p\)-adic groups. The papers are based on lectures presented at a conference dedicated to the memory of Larry Corwin and held at Rutgers University in February 1993. The book presents a survey of harmonic analysis on nilpotent homogeneous spaces, results on multiplicity formulas for induced representations, new methods for constructing unitary representations of real reductive groups, and a unified treatment of trace Paley-Wiener theorems for real and \(p\)-adic reductive groups. In the representation theory of the general linear group over \(p\)-adic fields, the book provides a description of Corwin's contributions, a survey of the role of Hecke algebras, and a presentation of the theory of simple types. Other types of reductive \(p\)-adic groups are also discussed. Among the other topics included are the representation theory of discrete rational nilpotent groups, skew-fields associated to quadratic algebras, and finite models for percolation. A timely publication featuring contributions by some of the top researchers in the field, this book offers a perspective not often found in conference proceedings.

Readership

Graduate students and researchers in the area of representations and harmonic analysis on real and \(p\)-adic Lie groups.

Table of Contents

• F. P. Greenleaf -- Harmonic analysis on nilpotent homogeneous spaces
• R. L. Lipsman -- Attributes and applications of the Corwin-Greenleaf multiplicity function
• C. Pfeffer-Johnston -- On unitary representations of some discrete rational nilpotent groups
• P. J. Sally, Jr. -- The work of Lawrence Corwin on the representation theory of reductive \(p\)-adic groups
• R. Howe -- Hecke algebras and \(p\)-adic \(GL_n\)
• D. Barbasch and A. Moy -- Whittaker models with an Iwahori fixed vector
• C. J. Bushnell and P. C. Kutzko -- Simple types in \(GL(N)\) : Computing conjugacy classes
• T. C. Hales -- Hyperelliptic curves and harmonic analysis
• J. Arthur -- The trace Paley Wiener theorem for Schwartz functions
• N. R. Wallach -- Transfer of unitary representations between real forms
• L. J. Corwin, I. M. Gel'fand, and R. Goodman -- Quadratic algebras and skew-fields
• R. P. Langlands and M.-A. Lafortune -- Finite models for percolation
• R. Goodman -- Lawrence J. Corwin
• R. Goodman -- Conference on representation theory and analysis on homogeneous spaces