  We evaluate the Geiss-Leclerc-Schroer $\phi$-map for shape modules over the
preprojective algebra $\Lambda$ of type $\hat{A_1}$ in terms of matrix minors
arising from the block-Toeplitz representation of the loop group
$\SL_2(\mathcal{L})$. Conjecturally these minors are among the cluster
variables for coordinate rings of unipotent cells within $\SL_2(\mathcal{L})$.
In so doing we compute the Euler characteristic of any generalized flag variety
attached to a shape module by counting standard tableaux of requisite shape and
parity; alternatively by counting chess tableaux of requisite shape and
content.
