Parabolic induction

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 is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of , 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.

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