  We study the Geroch group in the framework of the Ashtekar formulation. In
the case of the one-Killing-vector reduction, it turns out that the third
column of the Ashtekar connection is essentially the gradient of the Ernst
potential, which implies that the both quantities are based on the ``same''
complexification. In the two-Killing-vector reduction, we demonstrate Ehlers'
and Matzner-Misner's SL(2,R) symmetries, respectively, by constructing two sets
of canonical variables that realize either of the symmetries canonically, in
terms of the Ashtekar variables. The conserved charges associated with these
symmetries are explicitly obtained. We show that the gl(2,R) loop algebra
constructed previously in the loop representation is not the Lie algebra of the
Geroch group itself. We also point out that the recent argument on the
equivalence to a chiral model is based on a gauge-choice which cannot be
achieved generically.
