Titlebook: Representation Theory and Complex Geometry; Neil Chriss,Victor Ginzburg Book 2010 Birkh�user Boston 2010 D-modules.K-theory.algebraic geom

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Complex Semisimple Groups,We begin this section by reviewing some basic facts about semisimple groups and Lie algebras which we will need in the rest of this book. For further information the reader is referred to [Bour], [Bo3], [Hum], [Se1], and [Di].

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Springer Theory for , (sl,),ur point is that absolutely the same machinery can be applied to construct representations of sl.(C) and perhaps other semisimple Lie algebras, cf. [Na2]. Many of the objects we use for studying the sl.(C)-case are analogous to the objects in the Weyl group case.

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,Hecke Algebras and K–Theory,rking 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 .. ⊂ .., called the dual root system, and a specified bijection . ↔ .., α ↔ ᾰ are given such that the following three properties hold.

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Springer Theory for , (sl,),ur point is that absolutely the same machinery can be applied to construct representations of sl.(C) and perhaps other semisimple Lie algebras, cf. [Na2]. Many of the objects we use for studying the sl.(C)-case are analogous to the objects in the Weyl group case.