Langlands decomposition

Source: Wikipedia, the free encyclopedia.

In

product
of a reductive subgroup M, an abelian subgroup A, and a nilpotent subgroup N.

Applications

A 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 .

See also

  • Lie group decompositions

References

Sources

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