  In a recent work, Keith and Xiong gave a refinement of Glaisher's theorem by
using a Sylvester-style bijection. In this paper, we introduce two families of
colored partitions, flat and regular partitions, and generalize the bijection
of Keith and Xiong to these partitions. We then state two results, the first at
degree one, where partitions have parts with primary colors, and the second
result at degree two for secondary-colored partitions, using the result of the
first paper of this series. These results allow us to easily retrieve the
Frenkel-Kac character formulas of level one standard modules for the type
$A_{2n}^{(2)}, D_{n+1}^{(2)}$ and $B_n^{(1)}$, and also to make the connection
between the result stated in paper one and the representation theory.
