  We interpret a result of S. Oehms as a statement about the symplectic ideal.
We use this result to prove a double centraliser theorem for the symplectic
group acting on \bigoplus_{r=0}^s\otimes^rV, where V is the natural module for
the symplectic group. This result was obtained in characteristic zero by H.
Weyl. Furthermore we use this to extend to arbitrary connected reductive groups
G with simply connected derived group the earlier result of the author that the
algebra K[G]^g of infinitesimal invariants in the algebra of regular functions
on G is a unique factorisation domain.
