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Combinatorics of Minuscule Representations (Hardcover, New)
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Combinatorics of Minuscule Representations (Hardcover, New)
Series: Cambridge Tracts in Mathematics
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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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