  The symplectic group branching algebra, B, is a graded algebra whose
components encode the multiplicities of irreducible representations of
Sp(2n-2,C) in each irreducible representation of Sp(2n,C). By describing on B
an ASL structure, we construct an explicit standard monomial basis of B
consisting of Sp(2n-2,C) highest weight vectors. Moreover, B is known to carry
a canonical action of the n-fold product SL(2) \times ... \times SL(2), and we
show that the standard monomial basis is the unique (up to scalar) weight basis
associated to this representation. Finally, using the theory of Hibi algebras
we describe a deformation of Spec(B) into an explicit toric variety.
