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Combinatorics of Minuscule Representations (Cambridge Tracts by R. M. Green

By R. M. Green

Minuscule representations ensue in various contexts in arithmetic and physics. they're in general a lot more straightforward to appreciate than representations quite often, this means that they offer upward push to quite effortless structures of algebraic items similar to Lie algebras and Weyl teams. This ebook describes a combinatorial method of minuscule representations of Lie algebras utilizing the idea of lots, which for many sensible reasons should be considered yes labelled in part ordered units. This results in uniform structures of (most) uncomplicated Lie algebras over the advanced numbers and their linked Weyl teams, and offers a typical framework for varied purposes. the subjects studied contain Chevalley bases, permutation teams, weight polytopes and finite geometries. excellent as a reference, this ebook can be appropriate for college students with a heritage in linear and summary algebra and topology. each one bankruptcy concludes with ancient notes, references to the literature and recommendations for additional reading.

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