Non naturally reductive Einstein metrics on $\text{SU}(N)$ via generalized flag manifolds

We obtain new invariant Einstein metrics on the compact Lie group $\text{SU}(N)$ which are not naturally reductive. This is achieved by using the generalized flag manifold $G\mathrm{/}K=\text{SU}(k_1+\cdots +k_p)\mathrm{/}\text{s}(\text{U}(k_1)\times \cdots \times \text{U}(k_p))$ and by taking an appropriate choice of orthogonal basis of the center of Lie subalgebra $\mathfrak{k}$ for $K$, which poses certain symmetry conditions to the $\text{Ad}(K)$-invariant metrics of $\text{SU}(N)$. We also study the isometry problem for the Einstein metrics found.