  The present work is a part of a larger program to construct explicit
combinatorial models for the (indecomposable) regular representation of the
nilpotent factor $N$ in the Iwasawa decomposition of a semi-simple Lie algebra
$\mathfrak g$, using the restrictions to $N$ of the simple finite dimensional
modules of $\mathfrak g$. Such a description is given in \cite{[ABW]}, for the
cas $\mathfrak g=\mathfrak{sl}(n)$. Here, we give the analog for the rank 2
semi simple Lie algebras (of type $A_1\times A_1$, $A_2$, $C_2$ and $G_2$). The
algebra $\mathbb C[N]$ of polynomial functions on $N$ is a quotient, called
reduced shape algebra of the shape algebra for $\mathfrak g$. Basis for the
shape algebra are known, for instance the so called semi standard Young
tableaux (see \cite{[ADLMPPrW]}). We select among the semi standard tableaux,
the so called quasi standard ones which define a kind basis for the reduced
shape algebra.
