Abstract
We give a cohomological interpretation of both the Kac polynomial and the rened 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 isotypical 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.
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