  Let $W$ be the Weyl group of type $BC_n$. We first provide restriction
formulas of the total Springer representations for the symplectic Lie algebra
in characteristic 2 and the exotic case to the maximal parabolic subgroup of
$W$ which is of type $BC_{n-1}$. Then we show that these two restriction
formulas are equivalent, and discuss how the results can be used to examine the
existence of affine pavings of Springer fibers corresponding to the symplectic
Lie algebra in characteristic 2.
