EMS Series of Lectures in Mathematics 2011; 571 pp; softcover Volume: 13 ISBN10: 3037190809 ISBN13: 9783037190807 List Price: US$78 Member Price: US$62.40 Order Code: EMSSERLEC/13
 This book is an elementary selfcontained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourierlike integral operators such as SegalBargmann transforms, Gaussian integral operators in \(L^2\) and in the Fock space, integral operators with thetakernels, the geometry of real and \(p\)adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with thetafunctions and modular forms, \(p\)adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in representation theory, differential geometry, and operator theory. Table of Contents  Gaussian integral operators
 PseudoEuclidean geometry and groups \(\mathrm{U}(p, q)\)
 Linear symplectic geometry
 The SegalBargmann transform
 Gaussian operators in Fock spaces
 Gaussian operators. Details
 Hilbert spaces of holomorphic functions in matrix balls
 The Cartier model
 Gaussian operators over finite fields
 Classical \(p\)adic groups. Introduction
 Weil representation over a \(p\)adic field
 Addendum
 Bibliography
 Notation
 Index
