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Combinatorics of Minuscule Representations

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Title: Combinatorics of Minuscule Representations
Description: 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.
Authors: R. M. Green
Resource Type: eBook.
Subjects: Representations of Lie algebras, Combinatorial analysis
Categories: MATHEMATICS / Algebra / Intermediate
Database: eBook Collection (EBSCOhost)
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DbLabel: eBook Collection (EBSCOhost)
An: 529645
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PubType: eBook
PubTypeId: ebook
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  Data: Combinatorics of Minuscule Representations
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  Data: 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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    Classifications:
      – Code: 511.6
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Representations of Lie algebras
        Type: general
      – SubjectFull: Combinatorial analysis
        Type: general
    Titles:
      – TitleFull: Combinatorics of Minuscule Representations
        Type: main
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          Name:
            NameFull: R. M. Green
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2013
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9781107026247
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              Value: 9781107314443
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              Value: 00199
          Titles:
            – TitleFull: Combinatorics of Minuscule Representations
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