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This article studies components of Springer fibers for $\mathrm{𝔤𝔩}\left(n\right)$ that are associated to closed orbits of $GL\left(p\right)\times GL\left(q\right)$ on the flag variety of $GL\left(n\right),n=p+q$. These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of $GL\left(n\right)$. We prove that if $ℒ$ is a line bundle on the flag variety associated to a dominant weight, then the higher...