  Let k be an algebraically closed field of characteristic p>2. We compute the
Weyl filtration multiplicities in indecomposable tilting modules and the
decomposition numbers for the symplectic group over k in terms of cap-curl
diagrams under the assumption that p is bigger than the greatest hook length in
the largest partition involved. As a corollary we obtain the decomposition
numbers for the Brauer algebra under the same assumptions. Our work combines
ideas from work of Cox and De Visscher and work of Shalile with techniques from
the representation theory of reductive groups.
