  The branching coefficients of the tensor product of finite-dimensional
irreducible $U_{q}(\mathfrak{g})$-modules, where $\mathfrak{g}$ is
$\mathfrak{so}(2n+1,\mathbb{C})$ ($B_{n}$-type), $\mathfrak{sp}(2n,\mathbb{C})$
($C_{n}$-type), and $\mathfrak{so}(2n,\mathbb{C})$ ($D_{n}$-type), are
expressed in terms of Littlewood-Richardson (LR) coefficients in the stable
region. We give an interpretation of this relation by Kashiwara's crystal
theory by providing an explicit surjection from the LR crystal of type $C_{n}$
to the disjoint union of Cartesian product of LR crystals of $A_{n-1}$-type and
by proving that LR crystals of types $B_{n}$ and $D_{n}$ are identical to the
corresponding LR crystal of type $C_{n}$ in the stable region.
