Geometric Langlands duality and the equations of Nahm and Bogomolny

Geometric Langlands duality relates a representation of a simple Lie group G v to the cohomology of a certain moduli space associated with the dual group G. In this correspondence, a principal SL 2 subgroup of G v makes an unexpected appearance. This can be explained using gauge theory, as this paper will show, with the help of the equations of Nahm and Bogomolny.