Représentations de Weil et GL2 - Algèbres de division et GLn: Vers les corps de classes galoisiens I, II

This monograph represents the first two parts of the author's research on the generalization of class field theory for the noncommutative case. Part I concentrates on the construction of all the irreducible representations of a multiplicative group B* of a quaternion algebra B over a local field k with residue field of characteristic 2. These results are of considerable significance in the light of the connections found by Jacquet—Langlands between representations of GL2 (k) and B* and alth...