Algorithms in Invariant Theory
J. Kung and G.-C. Rota, in their 1984 paper, write: “Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics”. The book of Sturmfels is both an e
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Texts and Monographs in Symbolic Computation A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria Edited by P. Paule
Bernd Sturmfels Algorithms in Invariant Theory Second edition
SpringerWienNewYork
Dr. Bernd Sturmfels Department of Mathematics University of California, Berkeley, California, U.S.A.
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With 5 Figures
Library of Congress Control Number 2007941496
ISSN 0943-853X
ISBN 978-3-211-77416-8 SpringerWienNewYork ISBN 3-211-82445-6 1st edn. SpringerWienNewYork
Preface
The aim of this monograph is to provide an introduction to some fundamental problems, results and algorithms of invariant theory. The focus will be on the three following aspects: (i)
Algebraic algorithms in invariant theory, in particular algorithms arising from the theory of Gröbner bases; (ii) Combinatorial algorithms in invariant theory, such as the straightening algorithm, which relate to representation theory of the general linear group; (iii) Applications to projective geometry. Part of this material was covered in a graduate course which I taught at RISCLinz in the spring of 1989 and at Cornell University in the fall of 1989. The specific selection of topics has been determined by my personal taste and my belief that many interesting connections between invariant theory and symbolic computation are yet to be explored. In order to get started with her/his own explorations, the reader will find exercises at the end of each section. The exercises vary in difficulty. Some of them are easy and straightforward, while others are more difficult, and might in fact lead to research projects. Exercises which I consider “more difficult” are marked with a star. This book is intended for a diverse audience: graduate students who wish to learn the subject from scratch, researchers in the various fields of application who want to concentrate on certain aspects of the theory, specialists who need a reference on th
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