# Symmetry of Riemann Tensors via Group Actions.

It is a well known fact that the Riemann Curvature Tensor $${R^{\alpha}}_{\beta\gamma\lambda}$$ in $$n$$ dimensions have

$$\frac{n^2(n^2-1)}{12}$$

independent components. I have seen the combinatorial proof of this fact (for instance in this MS post or in Caroll's GR book section 3.7). I was wondering if there are easier ways of seeing this fact.

My question: Is there a way of seeing this formula in terms of group actions? (e.g. as some group acting on the space of tensors?)