Download e-book for kindle: Combinatorics of Minuscule Representations (Cambridge Tracts by R. M. Green

By R. M. Green

ISBN-10: 1107026245

ISBN-13: 9781107026247

Minuscule representations ensue in numerous contexts in arithmetic and physics. they're regularly a lot more straightforward to appreciate than representations commonly, this means that they provide upward thrust to rather effortless buildings of algebraic gadgets corresponding to Lie algebras and Weyl teams. This e-book describes a combinatorial method of minuscule representations of Lie algebras utilizing the idea of tons, which for many functional reasons could be regarded as sure labelled partly ordered units. This results in uniform structures of (most) uncomplicated Lie algebras over the complicated numbers and their linked Weyl teams, and offers a typical framework for numerous purposes. the themes studied contain Chevalley bases, permutation teams, weight polytopes and finite geometries. excellent as a reference, this e-book is usually compatible for college students with a historical past in linear and summary algebra and topology. each one bankruptcy concludes with ancient notes, references to the literature and proposals for extra reading.

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