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.
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978-0-8218-0300-4 (9780821803004)
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Schweitzer Klassifikation
Harmonic analysis on nilpotent homogeneous spaces by F. P. Greenleaf Attributes and applications of the Corwin-Greenleaf multiplicity function by R. L. Lipsman On unitary representations of some discrete rational nilpotent groups by C. Pfeffer-Johnston The work of Lawrence Corwin on the representation theory of reductive $p$-adic groups by P. J. Sally, Jr. Hecke algebras and $p$-adic $GL_n$ by R. Howe Whittaker models with an Iwahori fixed vector by D. Barbasch and A. Moy Simple types in $GL(N)$: Computing conjugacy classes by C. J. Bushnell and P. C. Kutzko Hyperelliptic curves and harmonic analysis by T. C. Hales The trace Paley Wiener theorem for Schwartz functions by J. Arthur Transfer of unitary representations between real forms by N. R. Wallach Quadratic algebras and skew-fields by L. J. Corwin, I. M. Gelfand, and R. Goodman Finite models for percolation by R. P. Langlands and M.-A. Lafortune Lawrence J. Corwin by R. Goodman Conference on representation theory and analysis on homogeneous spaces by R. Goodman.
