TY - JOUR
AB - 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.
AU - Tamas Hausel
AU - Letellier, Emmanuel
AU - RodrÃguez Villegas, Fernando
ID - 1442
IS - 3
JF - Annals of Mathematics
TI - Positivity for Kac polynomials and DT-invariants of quivers
VL - 177
ER -