Combinatorics of minuscule representations
 Author/Creator
 Green, R. M., 1971
 Language
 English.
 Publication
 Cambridge : Cambridge University Press, 2013.
 Copyright notice
 ©2013
 Physical description
 vii, 320 pages ; 24 cm.
 Series
 Cambridge tracts in mathematics ; 199.
Access
Available online

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QA252.3 .G74 2013

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QA252.3 .G74 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages 307310) and index.
 Contents

 Introduction 1. Classical Lie algebras and Weyl groups 2. Heaps over graphs 3. Weyl group actions 4. Lie theory 5. Minuscule representations 6. Full heaps over affine Dynkin diagrams 7. Chevalley bases 8. Combinatorics of Weyl groups 9. The 28 bitangents 10. Exceptional structures 11. Further topics Appendix A. Posets, graphs and categories Appendix B. Lie theoretic data References Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Minuscule representations occur in a variety of contexts in mathematics and physics. They are typically much easier to understand than representations in general, which means they give rise to relatively easy constructions of algebraic objects such as Lie algebras and Weyl groups. This book describes a combinatorial approach to minuscule representations of Lie algebras using the theory of heaps, which for most practical purposes can be thought of as certain labelled partially ordered sets. This leads to uniform constructions of (most) simple Lie algebras over the complex numbers and their associated Weyl groups, and provides a common framework for various applications. The topics studied include Chevalley bases, permutation groups, weight polytopes and finite geometries. Ideal as a reference, this book is also suitable for students with a background in linear and abstract algebra and topology. Each chapter concludes with historical notes, references to the literature and suggestions for further reading.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 R.M. Green, University of Colorado, Boulder.
 Series
 Cambridge tracts in mathematics ; 199
 ISBN
 9781107026247 (hardback)
 1107026245 (hardback)