X-Nico

Polycyclic group

Anatoly Maltsev proved that solvable subgroups of the integer general linear group are polycyclic; and later Louis Auslander (1967) and Swan proved the converse, that any polycyclic group is up to isomorphism a group of integer matrices.

Robert Langlands

The book by Hervé Jacquet and Langlands on $GL(2)$ presented a theory of automorphic forms for the general linear group $GL(2)$, establishing among other things the Jacquet–Langlands correspondence showing that functoriality was capable of explaining very precisely how automorphic forms for $GL(2)$ related to those for quaternion algebras.

Ulrich Stuhler

In 1993, he—along with Gérard Laumon and Michael Rapoport—proved the local Langlands conjectures for the general linear group GL_n(K) for positive characteristic local fields K.

see also