Combinatorics of minuscule representations / R.M. Green, University of Colorado, Denver.

Format:

Book

Author/Creator:

Green, R. M., 1971- author.

Series:

Cambridge tracts in mathematics ; 199.

Cambridge tracts in mathematics ; 199

Language:

English

Subjects (All):

Representations of Lie algebras.

Combinatorial analysis.

Physical Description:

1 online resource (vii, 320 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2013.

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-23652-5

1-107-30576-4

1-107-30160-2

1-107-30669-8

1-107-30889-5

1-107-31224-8

1-299-00906-9

1-107-31444-5

1-139-20700-8

OCLC:

827210322