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

By R. M. Green

Minuscule representations happen in numerous contexts in arithmetic and physics. they're regularly a lot more straightforward to appreciate than representations mostly, this means that they offer upward thrust to really effortless structures of algebraic gadgets resembling Lie algebras and Weyl teams. This publication describes a combinatorial method of minuscule representations of Lie algebras utilizing the speculation of lots, which for many functional reasons should be considered definite labelled partly ordered units. This results in uniform buildings of (most) basic Lie algebras over the advanced 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 appropriate for college kids with a history in linear and summary algebra and topology. each 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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