  Let $\SF^a_\lambda$ be the degenerate symplectic flag variety. These are
projective singular irreducible $\bG_a^M$ degenerations of the classical flag
varieties for symplectic group $Sp_{2n}$. We give an explicit construction for
the varieties $\SF^a_\lambda$ and construct their desingularizations, similar
to the Bott-Samelson resolutions in the classical case. We prove that
$\SF^a_\la$ are normal locally complete intersections with terminal and
rational singularities. We also show that these varieties are Frobenius split.
Using the above mentioned results, we prove an analogue of the Borel-Weil-Bott
theorem and obtain a $q$-character formula for the characters of irreducible
$Sp_{2n}$-modules via the Atiyah-Bott-Lefschetz fixed points formula.
