  Using an innovative technique arising from the theory of symmetric spaces, we
obtain an approximate analytic solution of the Dorokhov-Mello-Pereyra-Kumar
(DMPK) equation in the insulating regime of a metallic carbon nanotube with
symplectic symmetry and an odd number of conducting channels. This symmetry
class is characterized by the presence of a perfectly conducting channel in the
limit of infinite length of the nanotube. The derivation of the DMPK equation
for this system has recently been performed by Takane, who also obtained the
average conductance both analytically and numerically. Using the Jacobian
corresponding to the transformation to radial coordinates and the
parameterization of the transfer matrix given by Takane, we identify the
ensemble of transfer matrices as the symmetric space of negative curvature
SO^*(4m+2)/[SU(2m+1)xU(1)] belonging to the DIII-odd Cartan class. We rederive
the leading-order correction to the conductance of the perfectly conducting
channel <log(delta g)> and its variance Var(log(delta g)). Our results are in
complete agreement with Takane's. In addition, our approach based on the
mapping to a symmetric space enables us to obtain new universal quantities: a
universal group theoretical expression for the ratio Var(log(delta
g)/<log(delta g)> and as a byproduct, a novel expression for the localization
length for the most general case of a symmetric space with BC_m root system, in
which all three types of roots are present.
