---
res:
bibo_abstract:
- We propose a general conjecture for the mixed Hodge polynomial of the generic
character varieties of representations of the fundamental group of a Riemann surface
of genus g to GLn(C) with fixed generic semisimple conjugacy classes at k punctures.
This conjecture generalizes the Cauchy identity for Macdonald polynomials and
is a common generalization of two formulas that we prove in this paper. The first
is a formula for the E-polynomial of these character varieties which we obtain
using the character table of GLn(Fq). We use this formula to compute the Euler
characteristic of character varieties. The second formula gives the Poincaré polynomial
of certain associated quiver varieties which we obtain using the character table
of gln(Fq). In the last main result we prove that the Poincaré polynomials of
the quiver varieties equal certain multiplicities in the tensor product of irreducible
characters of GLn(Fq). As a consequence we find a curious connection between Kac-Moody
algebras associated with comet-shaped, and typically wild, quivers and the representation
theory of GLn(Fq).@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Tamas
foaf_name: Tamas Hausel
foaf_surname: Hausel
foaf_workInfoHomepage: http://www.librecat.org/personId=4A0666D8-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Emmanuel
foaf_name: Letellier, Emmanuel
foaf_surname: Letellier
- foaf_Person:
foaf_givenName: Fernando
foaf_name: Rodríguez Villegas, Fernando
foaf_surname: Rodríguez Villegas
bibo_doi: 10.1215/00127094-1444258
bibo_issue: '2'
bibo_volume: 160
dct_date: 2011^xs_gYear
dct_publisher: Duke University Press@
dct_title: Arithmetic harmonic analysis on character and quiver varieties@
...