Langlands decomposition

In mathematics, the Langlands decomposition writes a parabolic subgroup P of a semisimple Lie group as a product 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 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 .

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See also
  • Lie group decompositions

References

    Sources
    • A. W. Knapp, Structure theory of semisimple Lie groups. ISBN 0-8218-0609-2.


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