  In this note we give an elementary proof of the space-like real analyticity
of solutions to a degenerate evolution problem that arises in the study of
fractional parabolic operators of the type $(\partial_t -
div_x(B(x)\nabla_x))^s$, $0<s<1$. Our primary interest is in the so-called
\emph{extension variable}. We show that weak solutions that are even in such
variable, are in fact real-analytic in the totality of the space variables. As
an application of this result we prove the weak unique continuation property
for nonlocal parabolic operators of the type above, where $B(x)$ is a uniformly
elliptic matrix-valued function with real-analytic entries.
