Combinatorics of Minuscule Representations

R. M. Green (University of Colorado Boulder)

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English

Cambridge University Press
21 February 2013

Algebra; Algebraic topology; Combinatorics & graph theory; Mathematical physics

Series: Cambridge Tracts in Mathematics

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.

By: R. M. Green (University of Colorado Boulder)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 199
Dimensions: Height: 231mm, Width: 155mm, Spine: 23mm
Weight: 610g
ISBN: 9781107026247
ISBN 10: 1107026245
Series: Cambridge Tracts in Mathematics
Pages: 330
Publication Date: 21 February 2013
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

R. M. Green is a Professor in the Department of Mathematics at the University of Colorado, Boulder. He is the author of about 50 papers, many of which concern the combinatorics of Coxeter groups and related topics.

Reviews for Combinatorics of Minuscule Representations

'This monograph could be read with profit not only by the specialist, but also by an interested graduate student with some background on Lie algebras.' Felipe Zaldivar, MAA Reviews (maa.org/publications/maa-reviews)