  In this paper, we first study the shape algebra and the reduced shape algebra
for the Lie superalgebra $\mathfrak{sl}(m,n)$. We define the quasistandard
tableaux, their collection is the diamond cone for $\mathfrak{sl}(m,n)$, which
is a combinatorial basis for the reduced shape algebra. We realize a bijection
between the set of semistandard tableaux with shape $\lambda$ and the set of
quasistandard tableaux with shape $\mu\leq\lambda$, by using the 'super jeu de
taquin' on skew semistandard tableaux. This gives the compatibility of the
diamond cone with the natural stratification of the reduced shape algebra.
