Cox rings of moduli of quasi parabolic principal bundles and the K-Pieri rule

Abstract

We study a toric degeneration of the Cox ring of the moduli of principal $S{L}_m(\mathbb{C})$ 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.

26 pages, 11 figures, final version

References in corpus (4)

• Coordinate rings for the moduli of $SL_2(\C)$ quasi-parabolic principal bundles on a curve and toric fiber products
• Conformal blocks revisited
• Toric Degenerations and tropical geometry of branching algebras
• The algebra of $S{L}_3(\mathbb{C})$ conformal blocks