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Combinatorics of Minuscule Representations,9781107026247
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Combinatorics of Minuscule Representations

by
ISBN13:

9781107026247

ISBN10:
1107026245
Format:
Hardcover
Pub. Date:
4/8/2013
Publisher(s):
Cambridge Univ Pr
List Price: $80.00

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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.


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