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

By R. M. Green

ISBN-10: 1107026245

ISBN-13: 9781107026247

Minuscule representations happen in quite a few contexts in arithmetic and physics. they're as a rule a lot more straightforward to appreciate than representations often, this means that they provide upward thrust to quite effortless structures of algebraic gadgets comparable to Lie algebras and Weyl teams. This publication describes a combinatorial method of minuscule representations of Lie algebras utilizing the idea of tons, which for many sensible reasons could be regarded as sure labelled in part ordered units. This ends up in uniform buildings of (most) easy Lie algebras over the complicated numbers and their linked Weyl teams, and gives a typical framework for numerous functions. the themes studied contain Chevalley bases, permutation teams, weight polytopes and finite geometries. excellent as a reference, this booklet is additionally compatible for college kids with a historical past in linear and summary algebra and topology. each one bankruptcy concludes with historic notes, references to the literature and proposals for additional reading.

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


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