Comptes Rendus
no. 3-4
Lie Algebras/Algebraic Geometry
Topology of character varieties and representations of quivers
[Topologie des variétés de caractères et représentations de carquois]

Présenté par : Gérard Laumon

Tamás Hausel1 ; Emmanuel Letellier2 ; Fernando Rodriguez Villegas3
1 University of Oxford, UK
2 LMNO, département de mathématiques, Université de Caen, BP 5186, 14032 Caen, France
3 Department of Mathematics, University of Texas at Austin, Texas, USA
Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 131-135.

Dans Hausel et al. (2008) [10] nous avons énoncé une conjecture qui généralise la formule de Cauchy pour les polynômes de Macdonald. Cette formule contient l'information sur les polynômes de Hodge mixtes des variétés de représentations du groupe fondamental d'une surface de Riemann épointée de genre g. Nous avons montré plusieurs résultats qui appuient notre conjecture. Ici nous présentons de nouveaux résultats qui sont des conséquences de ceux de Hausel et al. (2008) [10].

In Hausel et al. (2008) [10] we presented a conjecture generalizing the Cauchy formula for Macdonald polynomial. This conjecture encodes the mixed Hodge polynomials of the character varieties of representations of the fundamental group of a punctured Riemann surface of genus g. We proved several results which support this conjecture. Here we announce new results which are consequences of those in Hausel et al. (2008) [10].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.01.025
Tamás Hausel 1 ; Emmanuel Letellier 2 ; Fernando Rodriguez Villegas 3

1 University of Oxford, UK
2 LMNO, département de mathématiques, Université de Caen, BP 5186, 14032 Caen, France
3 Department of Mathematics, University of Texas at Austin, Texas, USA 
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Tamás Hausel; Emmanuel Letellier; Fernando Rodriguez Villegas. Topology of character varieties and representations of quivers. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 131-135. doi : 10.1016/j.crma.2010.01.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.025/

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[9] T. Hausel, Arithmetic harmonic analysis, Macdonald polynomials and the topology of the Riemann–Hilbert monodromy map, with an appendix by E. Letellier, in preparation

[10] T. Hausel; E. Letellier; F. Rodriguez-Villegas Arithmetic harmonic analysis on character and quiver varieties, 2008 | arXiv

[11] T. Hausel, E. Letellier, F. Rodriguez-Villegas, Arithmetic harmonic analysis on character and quiver varieties II, in preparation

[12] V. Kac Root systems, representations of quivers and invariant theory, Lecture Notes in Math., vol. 996, Springer-Verlag, 1982, pp. 74-108

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