Hecke Algebras and K–Theory

doi:https://doi.org/10.1007/978-0-8176-4938-8_8

Hecke Algebras and K–Theory

Neil Chriss,Victor Ginzburg-2009-10-30-Birkhäuser Boston eBooks

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TL;DRAbstract

Let R ⊂ P be a reduced (not necessarily finite) root system as defined, e.g., in 3.1.22. There is a slight difference with 3.1.22, since now we are working with lattices instead of vector spaces. This makes axiom 3.1.22(3) superfluous. Thus it is assumed only that, in addition to the above data, a subset R v ⊂ P v, called the dual root system, and a specified bijection R ↔ R v, α ↔ ᾰ are given such that the following three properties hold.

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Let R ⊂ P be a reduced (not necessarily finite) root system as defined, e.g., in 3.1.22. There is a slight difference with 3.1.22, since now we are working with lattices instead of vector spaces. This makes axiom 3.1.22(3) superfluous. Thus it is assumed only that, in addition to the above data, a subset R v ⊂ P v, called the dual root system, and a specified bijection R ↔ R v, α ↔ ᾰ are given such that the following three properties hold.

Keywords

BijectionMathematicsRoot (linguistics)AxiomDual (grammatical number)Pure mathematicsCombinatoricsAlgebra over a field

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