  Mathematical instanton bundles on $ P_3$ have their analogues in rank--$2n$
instanton bundles on odd dimensional projective spaces $ P_{2n+1}$. The
families of special instanton bundles on these spaces generalize the special
'tHooft bundles on $ P_3$. We prove that for a special symplectic instanton
bundle $ E$ on $ P_{2n+1}$ with $c_2=k$ $h^1End( E) = 4(3n-1) k +
(2n-5)(2n-1)$. Therefore the dimension of the moduli space of instanton bundles
grows linearly in $k$. The main difference with the well known case of $ P_3$
is that $h^2End( E)$ is nonzero, in fact we prove that it grows quadratically
in $k$. Special symplectic instanton bundles turn out to be singular points of
the moduli space. Such bundles $ E$ are $SL(2)$--invariant and the result is
obtained regarding the cohomology groups of $ E$ as $SL(2)$--representations.
