AffiliationDepartment of Mathematics, University of Arizona
MetadataShow full item record
PublisherOxford University Press (OUP)
CitationCherkis, S. A., & Hurtubise, J. (2021). Instantons and Bows for the Classical Groups. Quarterly Journal of Mathematics, 72(1–2), 339–386.
JournalQuarterly Journal of Mathematics
Rights© The Author(s) 2020. Published by Oxford University Press. All rights reserved.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractThe construction of Atiyah, Drinfeld, Hitchin and Manin provided complete description of all instantons on Euclidean four-space. It was extended by Kronheimer and Nakajima to instantons on ALE spaces, resolutions of orbifolds R4 Γ by a finite subgroup ΓSU(2). We consider a similar classification, in the holomorphic context, of instantons on some of the next spaces in the hierarchy, the ALF multi-Taub-NUT manifolds, showing how they tie in to the bow solutions to Nahm's equations via the Nahm correspondence. Recently Nakajima and Takayama constructed the Coulomb branch of the moduli space of vacua of a quiver gauge theory, tying them to the same space of bow solutions. One can view our construction as describing the same manifold as the Higgs branch of the mirror gauge theory as described by Cherkis, O'Hara and Saemann. Our construction also yields the monad construction of holomorphic instanton bundles on the multi-Taub-NUT space for any classical compact Lie structure group.
Note12 month embargo; published: 26 November 2020
VersionFinal accepted manuscript