Deformations of W algebras via quantum toroidal algebras
dc.contributor.author | Feigin, B. | |
dc.contributor.author | Jimbo, M. | |
dc.contributor.author | Mukhin, E. | |
dc.contributor.author | Vilkovisky, I. | |
dc.contributor.department | Mathematical Sciences, School of Science | en_US |
dc.date.accessioned | 2022-12-19T16:19:51Z | |
dc.date.available | 2022-12-19T16:19:51Z | |
dc.date.issued | 2021-06 | |
dc.description.abstract | We 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.version | Author's manuscript | en_US |
dc.identifier.citation | Feigin, 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/s00029-021-00663-0 | en_US |
dc.identifier.issn | 1022-1824, 1420-9020 | en_US |
dc.identifier.uri | https://hdl.handle.net/1805/30763 | |
dc.language.iso | en_US | en_US |
dc.publisher | Springer | en_US |
dc.relation.isversionof | 10.1007/s00029-021-00663-0 | en_US |
dc.relation.journal | Selecta Mathematica | en_US |
dc.rights | Publisher Policy | en_US |
dc.source | ArXiv | en_US |
dc.subject | Integrals of motion | en_US |
dc.subject | 17B37 | en_US |
dc.subject | Quantum toroidal algebra | en_US |
dc.title | Deformations of W algebras via quantum toroidal algebras | en_US |
dc.type | Article | en_US |
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