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

We study a toric degeneration of the Cox ring of the moduli of principal SLm(C) bundles on the projective line, with quasi parabolic data given by the the stabilizer of the highest weight vector in Cm and its dual m−1 (Cm). 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. Contents

• Type: Journal
• Year: 2016
• Where: JCT
• Authors: Christopher Manon
• Keywords: Computer Science, JCT 2016