It's of the nature of an induced representation construction—what in the greater classic theory of automorphic sorts were referred to as a 'lifting', recognized in Specific scenarios, and so is covariant (While a limited representation is contravariant). Makes an attempt to specify a direct building have only made some conditional outcomes.

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Broadly seen as the single most significant project in modern-day mathematical study, the Langlands software is described by Edward Frenkel as "a kind of grand unified theory of mathematics."[one]

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By way of example, in 1994, when Andrew Wiles confirmed that Langlands’ proposed duality holds for a certain class of examples, the result was his evidence of Fermat’s Previous Theorem, One of the most celebrated brings about the record of mathematics.

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Roughly Talking, the reciprocity conjecture offers a correspondence in between automorphic representations of a reductive team and homomorphisms from a Langlands group to an L-team. You will find several variants of this, in part because the definitions of Langlands group and L-team will not be fixed.

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