This IMF published paper by Ostry, Berg, and Tsangarides presents empirical evidence on the relationships between inequality, redistributon, and growth. From the executive summary:
Second, lower net inequality is robustly correlated with faster and more durable growth, for a given level of redistribution. These results are highly supportive of our earlier work.
And third, redistribution appears generally benign in terms of its impact on growth; only in extreme cases is there some evidence that it may have direct negative effects on growth. Thus the combined direct and indirect effects of redistribution—including the growth effects of the resulting lower inequality—are on average pro-growth.