說明 
1 online resource (vii, 320 pages) : digital, PDF file(s) 

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unmediated n rdamedia 

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系列 
Cambridge tracts in mathematics ; 199 

Cambridge tracts in mathematics ; 199

附註 
Title from publisher's bibliographic system (viewed on 05 Oct 2015) 

Classical Lie algebras and Weyl groups  Heaps over graphs  Weyl group actions  Lie theory  Minuscule representations  Full heaps over affine Dynkin diagrams  Chevalley bases  Combinatorics of Weyl groups  The 28 bitangents  Exceptional structures 

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 
主題 
Representations of Lie algebras


Combinatorial analysis

