  We show that Lusztig's conjecture on the irreducible characters of a
reductive algebraic group over a field of positive characteristic is equivalent
to the generic multiplicity conjecture, which gives a formula for the
Jordan-H"older multiplicities of baby Verma modules over the corresponding Lie
algebra. Then we give a short overview of a recent proof of the latter
conjecture for almost all base fields via the theory of sheaves on moment
graphs.
