  We prove a conjecture of Liu and Wang on the q-log-convexity of the
polynomial sequence $\{\sum_{k=0}^n{n\choose k}^2q^k\}_{n\geq 0}$. By using
Pieri's rule and the Jacobi-Trudi identity for Schur functions, we obtain an
expansion of a sum of products of elementary symmetric functions in terms of
Schur functions with nonnegative coefficients. Then the principal
specialization leads to the q-log-convexity. We also prove that a technical
condition of Liu and Wang holds for the squares of the binomial coefficients.
Hence we deduce that the linear transformation with respect to the triangular
array $\{{n\choose k}^2\}_{0\leq k\leq n}$ is log-convexity preserving.
