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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:139

Article

Manon, Christopher¹ 

[1] George Mason Univ, Dept Math, Fairfax, VA 22030 USA

关键词: Conformal blocks;    Pieri rule;    Toric degeneration;    Invariant theory;   

DOI  :  10.1016/j.jcta.2015.11.002

来源: Elsevier

【 摘 要 】

We study a toric degeneration of the Cox ring of the moduli of quasi-principal SLm(C) bundles on a marked projective line in the case where the parabolic data is chosen in the stabilizer of the highest weight vector in C-m or its dual representation Lambda(m-1)(C-m). The result of this degeneration is an affine semigroup algebra which is naturally related to the combinatorics of the K-Pleri rule from Kac-Moody representation theory. We find that this algebra is normal and Gorenstein, with a quadratic square-free Grobner basis. This implies that the Cox ring is Gorenstein and Koszul for generic choices of markings, and generalizes results of Castravet, Tevelev and Sturmfels, Xu. Along the way we describe a relationship between the Cox ring and a classical invariant ring studied by Weyl. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free