  We give a formula for the superdimension of a finite-dimensional simple
gl(m|n)-module using the Su-Zhang character formula. As a corollary, we obtain
a simple algebraic proof of a conjecture of Kac-Wakimoto for gl(m|n), namely, a
simple module has nonzero superdimension if and only if it has maximal degree
of atypicality. This conjecture was proven originally by Serganova using the
Duflo-Serganova associated variety.
