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Arithmetic harmonic analysis on character and quiver varieties

Arithmetic harmonic analysis on character and quiver varieties

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 …