Neha Patil (Editor)

Langlands decomposition

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In mathematics, the Langlands decomposition writes a parabolic subgroup P of a semisimple Lie group as a product P = M A N 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 G is a reductive algebraic group and P = M A N is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of M A , extending it to P by letting N act trivially, and inducing the result from P to G .

References

Langlands decomposition Wikipedia
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