  According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like
singularity reduces to a set of decoupled one-dimensional mechanical models at
each point in space. We point out that these models fall into a class of
conformal mechanical models first introduced by de Alfaro, Fubini and Furlan
(DFF). The deformation used by DFF to render the spectrum discrete corresponds
to a negative cosmological constant. The wave function of the universe is the
zero-energy eigenmode of the Hamiltonian, also known as the spherical vector of
the representation of the conformal group SO(1,2). A new class of conformal
quantum mechanical models is constructed, based on the quantization of
nilpotent coadjoint orbits, where the conformal group is enhanced to an ADE
non-compact group for which the spherical vector is known.
