The Detroit Symphony Orchestra is losing its top executive, just as it is trying to find a new music director and cope with a hefty financial shortfall. Emil Kang, who had earned praise as DSO president for his consensus-building skills and efforts at sharpening the orchestra’s artistic vision, resigned abruptly on Monday, without explanation. The orchestra’s new board chair has refused to comment on whether or not Kang was forced out, but another board member says that, at least, the board “as a group” did not ask for the resignation. Kang, 35, was one of the youngest administrators of an American symphony orchestra.