Abstract
We consider the quantum mechanics of a particle on the coset superspace
$SU(2|1)/[U(1)\times U(1)]$, which is a super-flag manifold with
$SU(2)/U(1)\cong S^2$ `body'. By incorporating the Wess-Zumino terms associated
with the $U(1)\times U(1)$ stability group, we obtain an exactly solvable
super-generalization of the Landau model for a charged particle on the sphere.
We solve this model using the factorization method. Remarkably, the physical
Hilbert space is finite-dimensional because the number of admissible Landau
levels is bounded by a combination of the U(1) charges. The level saturating
the bound has a wavefunction in a shortened, degenerate, irrep of $SU(2|1)$.