The relationship between characteristics of quantum channels and
the geometry of their respective sets can provide a useful insight
to some of their underlying properties. First we will discuss a special
class of random unitary channels, namely, the Schur maps. We then use the
generalization of these maps to motivate the study of what we call
Self-Dual quantum channels. Some preliminary geometric properties of the
set of such maps are investigated and compared to the geometry of the set
of Schur maps. Finally, some preliminary algebraic results are discussed
which involve the eigenvalues of Self-Dual quantum channels.