Rational Singularities, Quiver Moment Maps, and Representations of Surface Groups

Abstract

Abstract We prove using jet schemes that the zero loci of the moment maps for the quivers with one vertex and at least two loops have rational singularities. This implies that the spaces of representations of the fundamental group of a compact Riemann surface of genus at least two have rational singularities. This has consequences for the numbers of irreducible representations of the special linear groups over the integers and over the $p$-adic integers.