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Combinatorics of Minuscule Representations (Cambridge Tracts in Mathematics Book 199)

Combinatorics of Minuscule Representations (Cambridge Tracts in Mathematics Book 199)

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Combinatorics of Minuscule Representations (Cambridge Tracts in Mathematics Book 199)

Combinatorics of Minuscule Representations (Cambridge Tracts in Mathematics Book 199)

Category

Math

Physics

Author

R. M. Green

Professor R. M. Green

Publication

Cambridge University Press

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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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9781107026247

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Cambridge University Press

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51.06

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R. M. Green

Discover more of the author’s books, see similar authors, read author blogs and more ...

Professor R. M. Green

Professor R. M. Green

Discover more of the author’s books, see similar authors, read author blogs and more ...

Review

"This monograph could be read with profit not only by the specialist, but also by an interested graduate student with some background on Lie algebras."
Felipe Zaldivar, MAA Reviews

"The exposition [is] very clear. The book is strongly recommended to students and researchers who are interested in combinatorial aspects of representation theory."
Hiro-Fumi Yamada, Mathematical Reviews

" useful as a book for students, the book under review is particularly useful as a reference for researchers of relevant fields."
Qendrim R. Gashi, Zentralblatt MATH --This text refers to the hardcover edition.

Book Description

Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups. --This text refers to the hardcover edition.

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