Abstract
Let G be a reductive connected algebraic group defined over a number field F. Fix a minimal parabolic subgroup P0 and a Levi component \(M_{P_{0}}\) of P0, both defined over F. In this chapter we work only with standard parabolic subgroups of G, that is, parabolic subgroups P, defined over F, which contain P0. We shall refer from now on to such groups simply as “parabolic subgroups.” Fix P. Let N P be the unipotent radical of P. Let M P be the unique Levi component of P which contains \(M_{P_{0}}\). Denote the split component of the center of M P by A P . The groups N P and A P are defined over F.
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