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Combinatorics of minuscule represent...

Green, R. M., (1971-)

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Combinatorics of minuscule representations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Combinatorics of minuscule representations/ R.M. Green, University of Colorado, Denver.
Author:	Green, R. M.,
Published:	Cambridge :Cambridge University Press, : 2013.,
Description:	vii, 320 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	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.
Subject:	Representations of Lie algebras. -
Online resource:	https://doi.org/10.1017/CBO9781139207003
ISBN:	9781139207003

Combinatorics of minuscule representations
Green, R. M.,1971-

Combinatorics of minuscule representations[electronic resource] /R.M. Green, University of Colorado, Denver. - Cambridge :Cambridge University Press,2013. - vii, 320 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;199. - Cambridge tracts in mathematics ;199..

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.

ISBN: 9781139207003Subjects--Topical Terms:

950288
Representations of Lie algebras.

LC Class. No.: QA252.3 / .G74 2013

Dewey Class. No.: 512.482

Combinatorics of minuscule representations
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100 1 $a Green, R. M., $d 1971- $3 2010672
245 1 0 $a Combinatorics of minuscule representations $h [electronic resource] / $c R.M. Green, University of Colorado, Denver.
260 $a Cambridge : $b Cambridge University Press, $c 2013.
300 $a vii, 320 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 199
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Representations of Lie algebras. $3 950288
650 0 $a Combinatorial analysis. $3 523878
830 0 $a Cambridge tracts in mathematics ; $v 199. $3 3470473
856 4 0 $u https://doi.org/10.1017/CBO9781139207003