  We show that the $\g$-vector of the interval subdivision of a simplicial
complex with a nonnegative and symmetric $h$-vector is nonnegative. In
particular, we prove that such $\g$-vector is the $f$-vector of some balanced
simplicial complex. Moreover, we show that the local $\g$-vector of the
interval subdivision of a simplex is nonnegative; answering a question by
Juhnke-Kubitzke et al.
