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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aCombinatorics of minuscule representations /$fR.M. Green, University of Colorado, Denver$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2013.
215   $a1 online resource (vii, 320 pages) $cdigital, PDF file(s)
225 1 $aCambridge tracts in mathematics ;$v199
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a1-107-02624-5 
320   $aIncludes bibliographical references and index.
327   $aClassical 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.
330   $aMinuscule representations occur in a variety of contexts in mathematics and physics. They are typically much easier to understand than representations in general, which means they give rise to relatively easy constructions of algebraic objects such as Lie algebras and Weyl groups. This book describes a combinatorial approach to minuscule representations of Lie algebras using the theory of heaps, which for most practical purposes can be thought of as certain labelled partially ordered sets. This leads to uniform constructions of (most) simple Lie algebras over the complex numbers and their associated Weyl groups, and provides a common framework for various applications. The topics studied include Chevalley bases, permutation groups, weight polytopes and finite geometries. Ideal as a reference, this book is also suitable for students with a background in linear and abstract algebra and topology. Each chapter concludes with historical notes, references to the literature and suggestions for further reading.
410  0$aCambridge tracts in mathematics ;$v199.
606   $aRepresentations of Lie algebras
606   $aCombinatorial analysis
615  0$aRepresentations of Lie algebras.
615  0$aCombinatorial analysis.
676   $a512/.482
686   $aMAT002000$2bisacsh
700   $aGreen$b R. M.$f1971-$01607847
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910809560003321
996   $aCombinatorics of minuscule representations$93934280
997   $aUNINA