By R. M. Green

Minuscule representations happen in various contexts in arithmetic and physics. they're in general a lot more straightforward to appreciate than representations mostly, this means that they provide upward thrust to particularly effortless structures of algebraic gadgets resembling Lie algebras and Weyl teams. This booklet describes a combinatorial method of minuscule representations of Lie algebras utilizing the speculation of lots, which for many sensible reasons may be regarded as convinced labelled partly ordered units. This results in uniform buildings of (most) basic Lie algebras over the advanced numbers and their linked Weyl teams, and offers a standard framework for varied functions. the subjects studied contain Chevalley bases, permutation teams, weight polytopes and finite geometries. excellent as a reference, this ebook is usually compatible for college kids with a history in linear and summary algebra and topology. every one bankruptcy concludes with historic notes, references to the literature and proposals for extra analyzing.

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