Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are'geo­ metrically indistinguishable,'that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub­ sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda­ mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.

scihub/10.1007/978-1-4757-1869-0.pdf

zlib/no-category/null/GTM99-Finite Reflection Groups1985_29509638.pdf

null

Springer London, Limited

Graduate Texts in Mathematics, A Selection, 99, Second edition, New York, NY, 1985

Springer Nature (Textbooks & Major Reference Works), New York, NY, 2013

United States, United States of America

sm41110422

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Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geoƯ metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the subƯ sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and fundaƯ mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B.L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude

2015-06-15