Structure of Reductive Groups
By studying the actions of tori and their centralizers on G/B, we showed in Chapter IX that a reductive group is generated by the centralizers of singular tori (the latter being precisely the connected kernels of roots). Moreover, we showed that the quotient of such a centralizer by its center is essentially PGL(2, K). The goal of this chapter is a more detailed description of G: properties of the root system, structure of normal subgroups of G, “normal form” for elements of G, structure of parabolic subgroups.
KeywordsNormal Subgroup Algebraic Group Weyl Group Parabolic Subgroup Reductive Group
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