On a conductor formula of Bushnell, Henniart and Kutzko

The explicit conductor formula of Bushnell, Henniart and Kutzko [BHK98] computes the conductor of a pair of supercuspidal representations of general linear groups over a non-archimedean local field in terms of inducing data for these representations. There are essentially two cases to consider, depending on whether a supercuspidal type admits a split cover or not. The strategy in [BHK98] is to deal with the split case first and to reduce the non-split case to the split case. In this paper, we give a direct proof of the non-split (self-dual) case of the conductor formula