  We show that there is a remarkable connection between the harmonic superspace
(HSS) formulation of N=2, d=4 supersymmetric quaternionic Kaehler sigma models
that couple to N=2 supergravity and the minimal unitary representations of
their isometry groups. In particular, for N=2 sigma models with quaternionic
symmetric target spaces of the form G/HXSU(2) we establish a one-to-one mapping
between the Killing potentials that generate the isometry group G under Poisson
brackets in the HSS formulation and the generators of the minimal unitary
representation of G obtained by quantization of its geometric realization as a
quasiconformal group. Quasiconformal extensions of U-duality groups of four
dimensional N=2, d=4 Maxwell-Einstein supergravity theories (MESGT) had been
proposed as spectrum generating symmetry groups earlier. We discuss some of the
implications of our results, in particular, for the BPS black hole spectra of
4d, N=2 MESGTs.
