@article{1442,
abstract = {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. Thisis 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 Poincare 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.},
author = {Tamas Hausel and Letellier, Emmanuel and RodrÃguez Villegas, Fernando},
journal = {Annals of Mathematics},
number = {3},
pages = {1147 -- 1168},
publisher = {Princeton University Press},
title = {{Positivity for Kac polynomials and DT-invariants of quivers}},
doi = {10.4007/annals.2013.177.3.8},
volume = {177},
year = {2013},
}