  Losev introduced the scheme $X$ of almost commuting elements (i.e., elements
commuting upto a rank one element) of $\mathfrak{g}=\mathfrak{sp}(V)$ for a
symplectic vector space $V$ and discussed its algebro-geometric properties. We
construct a Lagrangian subscheme $X^{nil}$ of $X$ and show that it is a
complete intersection of dimension
$\text{dim}(\mathfrak{g})+\frac{1}{2}\text{dim}(V)$ and compute its irreducible
components.
  We also study the quantum Hamiltonian reduction of the algebra
$\mathcal{D}(\mathfrak{g})$ of differential operators on the Lie algebra
$\mathfrak{g}$ tensored with the Weyl algebra with respect to the action of the
symplectic group, and show that it is isomorphic to the spherical subalgebra of
a certain rational Cherednik algebra of Type $C$.
