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作者 Green, R. M., 1971- author
書名 Combinatorics of minuscule representations / R.M. Green, University of Colorado, Denver
出版項 Cambridge : Cambridge University Press, 2013
國際標準書號 9781139207003 (electronic bk.)
9781107026247 (paper)
book jacket
說明 1 online resource (vii, 320 pages) : digital, PDF file(s)
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
text file PDF rda
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
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