The cohomology of free loop spaces of rank 2 flag manifolds

A complete flag manifold is the quotient of a Lie group by its maximal torus. The rank of a flag manifold is the dimension of the maximal torus of the Lie group. The rank 2 complete flag manifolds are $SU(3)\mathrm{/}{T}^2$, $Sp(2)\mathrm{/}{T}^2$, $Spin(4)\mathrm{/}{T}^2$, $Spin(5)\mathrm{/}{T}^2$ and $G_2\mathrm{/}{T}^2$. In this paper we calculate the cohomology of the free loop space of rank 2 complete flag manifolds.