The local Langlands correspondence can be seen as a non abelian generalization of class field theory. Roughly, it is a correspondence between the "Galois side" of finite dimensional representations of the Weil group $W_F$, F a local field, and the "admissible side" of admissible representations of $GL_n(F)$. In this talk we will address base change and automorphic induction using the K-theory of the reduced group C*-algebra $C^*_r(GLn_(F))$. The Langlands correspondence will then be used to create a structure of a complex algebraic variety on the admissible dual of GLn(F) as in [1].

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Langlands correspondence,functoriality,K-theory.

• Mathematics - Natural Sciences