Applications
See also: Parabolic inductionA key application is in parabolic induction, which leads to the Langlands program: if 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 by letting act trivially, and inducing the result from to .
Read more about this topic: Langlands Decomposition