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

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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

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References

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Sources

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