Show simple item record

dc.contributor.authorYoung, Charles A. S.
dc.date.accessioned2021-09-22T13:00:01Z
dc.date.available2021-09-22T13:00:01Z
dc.date.issued2021-12-01
dc.identifier.citationYoung , C A S 2021 , ' Affine opers and conformal affine Toda ' , Journal of the London Mathematical Society , vol. 104 , no. 5 , pp. 2148-2207 . https://doi.org/10.1112/jlms.12494
dc.identifier.issn1469-7750
dc.identifier.otherJisc: ffd8d27c5d2d4d4d83f7926ed5a18440
dc.identifier.otherJisc: ffd8d27c5d2d4d4d83f7926ed5a18440
dc.identifier.otherpublisher-id: jlms12494
dc.identifier.otherORCID: /0000-0002-7490-1122/work/133139407
dc.identifier.urihttp://hdl.handle.net/2299/25074
dc.description© 2021 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, https://creativecommons.org/licenses/by/4.0/, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
dc.description.abstractAbstract: For g a Kac–Moody algebra of affine type, we show that there is an Aut O ‐equivariant identification between Fun Op g ( D ) , the algebra of functions on the space of g ‐opers on the disc, and W ⊂ π 0 , the intersection of kernels of screenings inside a vacuum Fock module π 0 . This kernel W is generated by two states: a conformal vector and a state δ − 1 | 0 > . We show that the latter endows π 0 with a canonical notion of translation T ( aff ) , and use it to define the densities in π 0 of integrals of motion of classical Conformal Affine Toda field theory. The Aut O ‐action defines a bundle Π over P 1 with fibre π 0 . We show that the product bundles Π ⊗ Ω j , where Ω j are tensor powers of the canonical bundle, come endowed with a one‐parameter family of holomorphic connections, ∇ ( aff ) − α T ( aff ) , α ∈ C . The integrals of motion of Conformal Affine Toda define global sections [ v j d t j + 1 ] ∈ H 1 ( P 1 , Π ⊗ Ω j , ∇ ( aff ) ) of the de Rham cohomology of ∇ ( aff ) . Any choice of g ‐Miura oper χ gives a connection ∇ χ ( aff ) on Ω j . Using coinvariants, we define a map F χ from sections of Π ⊗ Ω j to sections of Ω j . We show that F χ ∇ ( aff ) = ∇ χ ( aff ) F χ , so that F χ descends to a well‐defined map of cohomologies. Under this map, the classes [ v j d t j + 1 ] are sent to the classes in H 1 ( P 1 , Ω j , ∇ χ ( aff ) ) defined by the g ‐oper underlying χ .en
dc.format.extent60
dc.format.extent884456
dc.language.isoeng
dc.relation.ispartofJournal of the London Mathematical Society
dc.subjectResearch Article
dc.subjectResearch Articles
dc.subject17B69
dc.subject81R10
dc.subject81R12 (primary)
dc.subject17B67 (secondary)
dc.subjectMathematics(all)
dc.titleAffine opers and conformal affine Todaen
dc.contributor.institutionDepartment of Physics, Astronomy and Mathematics
dc.contributor.institutionSchool of Physics, Engineering & Computer Science
dc.contributor.institutionMathematics and Theoretical Physics
dc.description.statusPeer reviewed
dc.identifier.urlhttp://www.scopus.com/inward/record.url?scp=85114649110&partnerID=8YFLogxK
rioxxterms.versionofrecord10.1112/jlms.12494
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record