dc.contributor.author | Young, Charles A. S. | |
dc.date.accessioned | 2021-09-22T13:00:01Z | |
dc.date.available | 2021-09-22T13:00:01Z | |
dc.date.issued | 2021-12-01 | |
dc.identifier.citation | Young , 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.issn | 1469-7750 | |
dc.identifier.other | Jisc: ffd8d27c5d2d4d4d83f7926ed5a18440 | |
dc.identifier.other | Jisc: ffd8d27c5d2d4d4d83f7926ed5a18440 | |
dc.identifier.other | publisher-id: jlms12494 | |
dc.identifier.other | ORCID: /0000-0002-7490-1122/work/133139407 | |
dc.identifier.uri | http://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.abstract | Abstract: 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.extent | 60 | |
dc.format.extent | 884456 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the London Mathematical Society | |
dc.subject | Research Article | |
dc.subject | Research Articles | |
dc.subject | 17B69 | |
dc.subject | 81R10 | |
dc.subject | 81R12 (primary) | |
dc.subject | 17B67 (secondary) | |
dc.subject | General Mathematics | |
dc.title | Affine opers and conformal affine Toda | en |
dc.contributor.institution | Department of Physics, Astronomy and Mathematics | |
dc.contributor.institution | School of Physics, Engineering & Computer Science | |
dc.contributor.institution | Mathematics and Theoretical Physics | |
dc.description.status | Peer reviewed | |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=85114649110&partnerID=8YFLogxK | |
rioxxterms.versionofrecord | 10.1112/jlms.12494 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |