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

By R. M. Green

ISBN-10: 1107026245

ISBN-13: 9781107026247

Minuscule representations ensue in numerous 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 fairly effortless structures of algebraic items akin to Lie algebras and Weyl teams. This ebook describes a combinatorial method of minuscule representations of Lie algebras utilizing the speculation of tons, which for many useful reasons could be regarded as definite labelled partly ordered units. This ends up in uniform structures of (most) basic Lie algebras over the complicated numbers and their linked Weyl teams, and offers a typical framework for varied functions. the subjects studied comprise Chevalley bases, permutation teams, weight polytopes and finite geometries. excellent as a reference, this publication is usually appropriate for college students with a historical past in linear and summary algebra and topology. every one bankruptcy concludes with old notes, references to the literature and proposals for extra reading.

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

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