Langlands Program. To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a fin

Langlands Program. To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a finite field with its group extension to the automorphic forms under which it is invariant. This is accomplished through abstraction to higher dimensional integration, by an equivalence to a certain analytical group as an absolute extension of its algebra. Consequently, this allows an analytical functional construction of powerful invariance transformations for a number field to its own algebraic structure. https://en.wikipedia.org/wiki/Langlands_program https://en.wikipedia.org/wiki/Langlands_program