  We give a cohomological interpretation of both the Kac polynomial and the
refined Donaldson-Thomas- invariants of quivers. This interpretation yields a
proof of a conjecture of Kac from 1982 and gives a new perspective on recent
work of Kontsevich-Soibelman. This is achieved by computing, via an arithmetic
Fourier transform, the dimensions of the isoytpical components of the
cohomology of associated Nakajima quiver varieties under the action of a Weyl
group. The generating function of the corresponding Poincar\'e polynomials is
an extension of Hua's formula for Kac polynomials of quivers involving
Hall-Littlewood symmetric functions. The resulting formulae contain a wide
range of information on the geometry of the quiver varieties.
