Reflection Groups and Invariant Theory
Reflection Groups and Invariant Theory by Richard Kane, published by Springer Science & Business Media on June 21, 2001, is a comprehensive exploration of reflection groups and their invariant theory. This edition spans 379 pages and is presented in English, making it accessible to a wide audience. The book is structured into three main parts, with the first focusing on reflection groups, including Coxeter and Weyl groups, within Euclidean space. The subsequent chapters delve into the invariant theory of pseudo-reflection groups, culminating in a study of conjugacy classes related to these groups.
Readers will find that the text is designed as a graduate-level resource, suitable for those with a foundational understanding of algebra. The content reflects the author’s extensive experience teaching graduate courses over the past decade, ensuring that complex concepts are presented in a clear and structured manner. Topics such as group theory, mathematical analysis, and geometry are integral to the discussions throughout the book, providing a thorough grounding in the subject matter.
Official synopsis Publisher
Reflection Groups and their invariant theory provide the main themes of this book and the first two parts focus on these topics. The first 13 chapters deal with reflection groups (Coxeter groups and Weyl groups) in Euclidean Space while the next thirteen chapters study the invariant theory of pseudo-reflection groups. The third part of the book studies conjugacy classes of the elements in reflection and pseudo-reflection groups. The book has evolved from various graduate courses given by the author over the past 10 years. It is intended to be a graduate text, accessible to students with a basic background in algebra.
Richard Kane is a professor of mathematics at the University of Western Ontario. His research interests are algebra and algebraic topology. Professor Kane is a former President of the Canadian Mathematical Society.
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