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

Homology of analogues of Heisenberg Lie algebras