  The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition
series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described
by Serganova, leading to her solution of the character problem for gl(m/n). In
Serganova's algorithm all mu with nonzero a_{lambda,mu} are determined for a
given lambda; this algorithm turns out to be rather complicated. In this Letter
a simple rule is conjectured to find all nonzero a_{lambda,mu} for any given
weight mu. In particular, we claim that for an r-fold atypical weight mu there
are 2^r distinct weights lambda such that a_{lambda,mu}=1, and a_{lambda,mu}=0
for all other weights lambda. Some related properties on the multiplicities
a_{lambda,mu} are proved, and arguments in favour of our main conjecture are
given. Finally, an extension of the conjecture describing the inverse of the
matrix of Kazhdan-Lusztig polynomials is discussed.
