Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds

We obtain new invariant Einstein metrics on the compact Lie groups $\text{SO}(n)$ which are not naturally reductive. This is achieved by using the real flag manifolds $\text{SO}(k_1+\cdots +k_p)\mathrm{/}\text{SO}(k_1)\times \cdots \times \text{SO}(k_p)$ and by imposing certain symmetry assumptions in the set of all left-invariant metrics on $\text{SO}(n)$.