
Preface  Preview Material  Table of Contents  Supplementary Material 
Fields Institute Monographs 2011; 291 pp; hardcover Volume: 28 ISBN10: 0821842714 ISBN13: 9780821842713 List Price: US$99 Member Price: US$79.20 Order Code: FIM/28 See also: Representation Theory of Finite Groups: Algebra and Arithmetic  Steven H Weintraub Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer  Charles W Curtis Representations of Finite and Compact Groups  Barry Simon  Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematicslinear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian formsand thus inherit some of the characteristics of both. This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and WittGrothendieck groups, over the "classical" fieldsalgebraically closed, real closed, finite, local and global. A detailed exposition of the background material needed is given in the first chapter. It was A. Fröhlich who first gave a systematic organization of this subject, in a series of papers beginning in 1969. His paper Orthogonal and symplectic representations of groups represents the culmination of his published work on orthogonal and symplectic representations. The author has included most of the work from that paper, extending it to include unitary representations, and also providing new approaches, such as the use of the equivariant BrauerWall group in describing the principal invariants of orthogonal representations and their interplay with each other. Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in the representations of finite groups, surgery theory, or equivariant superalgebras. Reviews "This book is a most welcome introduction to this wonderful subject with deep roots in two classical areas of mathematics, collecting in one place the most recent developments. It can be profitably read by anyone interested with a basic background on representation theory and quadratic forms."  MAA Reviews 


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