Deformations of W algebras via quantum toroidal algebras

dc.contributor.authorFeigin, B.
dc.contributor.authorJimbo, M.
dc.contributor.authorMukhin, E.
dc.contributor.authorVilkovisky, I.
dc.contributor.departmentMathematical Sciences, School of Scienceen_US
dc.date.accessioned2022-12-19T16:19:51Z
dc.date.available2022-12-19T16:19:51Z
dc.date.issued2021-06
dc.description.abstractWe study the uniform description of deformed W algebras of type A including the supersymmetric case in terms of the quantum toroidal gl1 algebra E. In particular, we recover the deformed affine Cartan matrices and the deformed integrals of motion. We introduce a comodule algebra K over E which gives a uniform construction of basic deformed W currents and screening operators in types B,C,D including twisted and supersymmetric cases. We show that a completion of algebra K contains three commutative subalgebras. In particular, it allows us to obtain a commutative family of integrals of motion associated with affine Dynkin diagrams of all non-exceptional types except D(2)ℓ+1. We also obtain in a uniform way deformed finite and affine Cartan matrices in all classical types together with a number of new examples, and discuss the corresponding screening operators.en_US
dc.eprint.versionAuthor's manuscripten_US
dc.identifier.citationFeigin, B., Jimbo, M., Mukhin, E., & Vilkoviskiy, I. (2021). Deformations of W algebras via quantum toroidal algebras. Selecta Mathematica, 27(4), 52. https://doi.org/10.1007/s00029-021-00663-0en_US
dc.identifier.issn1022-1824, 1420-9020en_US
dc.identifier.urihttps://hdl.handle.net/1805/30763
dc.language.isoen_USen_US
dc.publisherSpringeren_US
dc.relation.isversionof10.1007/s00029-021-00663-0en_US
dc.relation.journalSelecta Mathematicaen_US
dc.rightsPublisher Policyen_US
dc.sourceArXiven_US
dc.subjectIntegrals of motionen_US
dc.subject17B37en_US
dc.subjectQuantum toroidal algebraen_US
dc.titleDeformations of W algebras via quantum toroidal algebrasen_US
dc.typeArticleen_US
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