  We give the first two-dimensional pictorial presentation of Berele's
correspondence \cite{Berele}, an analogue of the Robinson-Schensted (R-S)
correspondence \cite{Robinson, Schensted} for the symplectic group $Sp(2n, \Cpx
)$. From the standpoint of representation theory, the R-S correspondence
combinatorially describes the irreducible decomposition of the tensor powers of
the natural representation of $GL(n,\Cpx)$. Berele's insertion algorithm gives
the bijection that describes the irreducible decomposition of the tensor powers
of the natural representation of $Sp(2n, \Cpx)$. Two-dimensional pictorial
presentations of the R-S correspondence via local rules (first given by S.
Fomin \cite{Fomin,FominGen}) and its many variants have proven very useful in
understanding their properties and creating new generalizations. We hope our
new presentation will be similarly useful.
