LOOP GROUPS AND HOLOMORPHIC BUNDLES

DOI10.1093/QMATH/HAR037zbMATH Open1279.22031arXiv0812.3684OpenAlexW2144838005MaRDI QIDQ4914428

Michael K. Murray, Jacques Hurtubise

Publication date: 19 April 2013

Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)

Abstract: This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of G-bundles with additional flag structure along a line is proven for any reductive group; this gives the corresponding stability statement for any compact group K for the moduli of K-instantons over the four-sphere, and for the moduli of K-calorons over the three-sphere times the circle. The paper also considers the Hecke transforms on bundles induced by outer automorphisms of the loop groups.

Full work available at URL: https://arxiv.org/abs/0812.3684

zbMATH Keywords

vector bundlesmoduli spacesloop groupsglobal analysisalgebraic geometryinfinite-dimensional Lie groupsfunctions of several complex variables

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65)

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