  We prove that the numbers of irreducible n-dimensional complex continuous
representations of the special linear groups over p-adic integers grow slower
than the square of n. We deduce that the abscissas of convergence of the
representation zeta functions of the special linear groups over the ring of
integers are bounded above by 2. In order to show these results we prove also
that if G is a connected, simply connected, semi-simple algebraic group defined
over the field of rational numbers, then the G-representation variety of the
fundamental group of a compact Riemann surface of genus n has rational
singularities if and only if the G-character variety has rational
singularities.
