  The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be
defined in terms of the large time decay of the heat operator of the Laplacian
on square integrable p-forms on M. For the (2n+1)-dimensional Heisenberg group
H, the Laplacian can be decomposed into operators in the conjugate of the
generalised Bargmann representations which, when restricted to the centre of H,
are characters. The representation space is an anti-Fock space of
anti-holomorphic functions on complex n-space which are square integrable with
respect to a Gaussian measure. In this paper, the eigenvalues of decomposed
operators are calculated, using operators which commute with the Laplacian;
this information determines all the Novikov-Shubin invariants of H. Further,
some eigenvalues of operators connected with nilpotent Lie groups of Heisenberg
type are calculated in the later sections.
