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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups.If G is a reductive algebraic group and P = MAN is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of MA, extending it to P by letting N act trivially, and inducing the result from P to G.There are some generalizations of parabolic induction using cohomology, such as cohomological parabolic induction and Deligne Lusztig theory.