  We calculate the homology of three families of 2-step nilpotent Lie
(super)algebras associated with the symplectic, orthogonal, and general linear
groups. The symplectic case was considered by Getzler and the main motivation
for this work was to complete the calculations started by him. In all three
cases, these algebras can be realized as the nilpotent radical of a parabolic
subalgebra of a simple Lie algebra, and our first approach relies on a theorem
of Kostant, but is otherwise elementary and involves combinatorics of Weyl
groups and partitions which may be of independent interest. Our second approach
is an application of (un)stable representation theory of the classical groups
in the sense of recent joint work of the author with Snowden, which is shorter
and more conceptual.
