Dimensions of orthosymplectic nilpotent orbits

We begin to generalize to good prime characteristic the results of Kraft and Procesi in their 1982 paper, “On the geometry of conjugacy classes in classical groups,” that describe which nilpotent orbits of an orthogonal or symplectic Lie algebra have normal closure. The first step is to modify the proof of a dimension formula for orthosymplectic orbits to be independent of the characteristic of the base field, excluding characteristic 2. This is accomplished by explicit construction of an appropriate cocharacter, which we show exists in the particular setting of the problem, relying heavily on the description of orthosymplectic orbits via ab-diagrams, an analogue of Young diagrams.