Geodesic
Positivity for Kac polynomials and DT-invariants of quivers
Tamás Hausel1 ; Emmanuel Letellier2 ; Fernando Rodriguez-Villegas3
1 École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
2 Laboratoire LMNO<br/> Université de Caen, 14032 Caen, France
3 Department of Mathematics, University of Texas at Austin, 78712 Austin, TX, and International Centre for Theoretical Physics, Strada Costiera, 11, 34151 Trieste, Italy
Annals of mathematics, Tome 177 (2013) no. 3, pp. 1147-1168.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 Poincaré 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.
DOI : 10.4007/annals.2013.177.3.8

Tamás Hausel 1 ; Emmanuel Letellier 2 ; Fernando Rodriguez-Villegas 3

1 École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
2 Laboratoire LMNO<br/> Université de Caen, 14032 Caen, France
3 Department of Mathematics, University of Texas at Austin, 78712 Austin, TX, and International Centre for Theoretical Physics, Strada Costiera, 11, 34151 Trieste, Italy 
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Tamás Hausel; Emmanuel Letellier; Fernando Rodriguez-Villegas. Positivity for  Kac polynomials and DT-invariants of quivers. Annals of mathematics, Tome 177 (2013) no. 3, pp. 1147-1168. doi : 10.4007/annals.2013.177.3.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.3.8/

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