Translations of Mathematical Monographs 1992; 245 pp; softcover Volume: 100 ISBN10: 082185335X ISBN13: 9780821853351 List Price: US$90 Member Price: US$72 Order Code: MMONO/100.S
 The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists. Readership Graduate students and research mathematicians interested in invariant theory. Reviews "The book is a good reference for specialists in invariant theory and stimulating for nonexperts."  Zentralblatt MATH Table of Contents  Introduction
 Notation and terminology
 The role of reductive groups in invariant theory
 Constructive invariant theory
 The degree of the Poincaré series of the algebra of invariants and a finiteness theorem for representations with free algebra of invariants
 Syzygies in invariant theory
 Representations with free modules of covariants
 A classification of normal affine quasihomogeneous varieties of \(SL_2\)
 Quasihomogeneous curves, surfaces, and solids
 Appendices
 Bibliography
 Subject index
