  In the first paper of this series, we gave infinite families of coloured
partition identities which generalise Primc's and Capparelli's classical
identities.
  In this second paper, we study the representation theoretic consequences of
our combinatorial results. First, we show that the difference conditions we
defined in our $n^2$-coloured generalisation of Primc's identity, which have a
very simple expression, are actually the energy function with values in
$\{0,1,2\}$ for the perfect crystal of the tensor product of the vector
representation and its dual in $A_{n-1}^{(1)}$.
  Then we introduce a new type of partitions, grounded partitions, which allows
us to retrieve connections between character formulas and partition generating
functions without having to perform a specialisation.
  Finally, using the formulas for the generating functions of our generalised
partitions, we recover the Kac-Peterson character formula for the characters of
all the irreducible highest weight $A_{n-1}^{(1)}$-modules of level $1$, and
give a new character formula as a sum of infinite products with obviously
positive coefficients in the generators $e^{- \alpha_i} \ (i \in \{0, \dots ,
n-1\}),$ where the $\alpha_i$'s are the simple roots.
