Positivity for Kac polynomials and DT-invariants of quivers

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 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.


Published in:
Annals Of Mathematics, 177, 3, 1147-1168
Year:
2013
Publisher:
Princeton, Annal Mathematics
ISSN:
0003-486X
Laboratories:




 Record created 2013-05-13, last modified 2018-03-17


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