Combinatorics of Minuscule Representations (Cambridge Tracts - download pdf or read online

By R. M. Green

ISBN-10: 1107026245

ISBN-13: 9781107026247

Minuscule representations ensue in numerous contexts in arithmetic and physics. they're usually a lot more straightforward to appreciate than representations normally, this means that they offer upward push to fairly effortless structures of algebraic gadgets corresponding to 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 useful reasons may be considered sure labelled in part ordered units. This ends up in uniform buildings of (most) uncomplicated Lie algebras over the advanced numbers and their linked Weyl teams, and offers a typical framework for varied purposes. the themes studied comprise Chevalley bases, permutation teams, weight polytopes and finite geometries. perfect as a reference, this publication is additionally compatible for college kids with a history in linear and summary algebra and topology. every one bankruptcy concludes with ancient notes, references to the literature and recommendations for extra reading.

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Combinatorics of Minuscule Representations (Cambridge Tracts in Mathematics, 199) by R. M. Green

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