Combinatorics of Minuscule Representations

R. M. Green

2013년 2월 · Cambridge Tracts in Mathematics 199권 · Cambridge University Press

eBook

329

페이지

검증되지 않은 평점과 리뷰입니다. 자세히 알아보기

eBook 정보

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.

저자 정보

R. M. Green is a Professor in the Department of Mathematics at the University of Colorado, Boulder. He is the author of about 50 papers, many of which concern the combinatorics of Coxeter groups and related topics.