Higgs bundles on weighted projective lines and loop crystals

2013/12/20 by Guillaume Pouchin, Pouchin, Guillaume
Mathematics · Physics and Astronomy · #05E10 #14H60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1312.5838

openalex publication_date 2013/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the space of nilpotent Higgs bundles on a weighted projective line, as a global analog of the nilpotent cone. We show that it is pure, compute its dimension, and define geometric correspondences between irreducible components. We prove it by constructing a loop analog of a cristal, in the spirit of Kashiwara and Saito, for some corresponding loop Kac-Moody algebra.

Citations

• Canonical bases of loop algebras via quot schemes II

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