  We study a toric degeneration of the Cox ring of the moduli of principal
$SL_m(\mathbb{C})$ bundles on the projective line, with quasi parabolic data
given by the the stabilizer of the highest weight vector in $\mathbb{C}^m$ and
its dual $\bigwedge^{m-1}(\mathbb{C}^m)$. The affine semigroup algebra
resulting from this degeneration is described using the $K-$Pieri rule from
Kac-Moody representation theory. Along the way we give a proof of the $K-$Pieri
rule which utilizes the classical Pieri rule and elements of commutative
algebra, and we describe a relationship between the Cox ring and a classical
invariant ring studied by Weyl.
