  In [11] we showed that a loop in a simply connected compact Lie group
$\dot{U}$ has a unique Birkhoff (or triangular) factorization if and only if
the loop has a unique root subgroup factorization (relative to a choice of a
reduced sequence of simple reflections in the affine Weyl group). In this paper
our main purpose is to investigate Birkhoff and root subgroup factorization for
loops in a noncompact type semisimple Lie group $\dot G_0$ of inner type. In
[4] we showed that for an element of $\dot G_0$, i.e. a constant loop, there is
a unique Birkhoff factorization if and only if there is a root subgroup
factorization. However for loops in $\dot G_0$, while a root subgroup
factorization implies a unique Birkhoff factorization, there are several
obstacles to the converse. As in the compact case, root subgroup factorization
is intimately related to factorization of Toeplitz determinants.
