Langlands decomposition explained

P = MAN of a reductive subgroup M, an abelian subgroup A, and a nilpotent subgroup N.

Applications

See also: Parabolic induction. A key application is in parabolic induction, which leads to the Langlands program: 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 .

See also

• Lie group decompositions

References

Sources

• A. W. Knapp, Structure theory of semisimple Lie groups. .