{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1362825896246289920.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1063/1.2823979"}},{"identifier":{"@type":"URI","@value":"https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/1.2823979/16652468/123520_1_online.pdf"}}],"dc:title":[{"@value":"A (q,γ) analog of the W1+∞ algebra"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p>A (q,γ) analog of the W1+∞ algebra is introduced. Irreducible quasifinite highest weight modules of this algebra and R matrices acting on a tensor product of these modules are investigated. A connection with the q deformed Virasoro and WN algebras is also discussed.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1382825896246289920","@type":"Researcher","foaf:name":[{"@value":"Kei Miki"}],"jpcoar:affiliationName":[{"@value":"Osaka University Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, , Toyonaka 560-0043, Japan"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"00222488"},{"@type":"EISSN","@value":"10897658"}],"prism:publicationName":[{"@value":"Journal of Mathematical Physics"}],"dc:publisher":[{"@value":"AIP Publishing"}],"prism:publicationDate":"2007-12-01","prism:volume":"48","prism:number":"12","prism:startingPage":"123520"},"reviewed":"false","url":[{"@id":"https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/1.2823979/16652468/123520_1_online.pdf"}],"createdAt":"2007-12-28","modifiedAt":"2023-08-02","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360004231128992768","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Extended conformal symmetry and recursion formulae for Nekrasov partition function"}]},{"@id":"https://cir.nii.ac.jp/crid/1360004234611305728","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"CFT approach to the q-Painlevé VI equation"}]},{"@id":"https://cir.nii.ac.jp/crid/1360009142646232448","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function"}]},{"@id":"https://cir.nii.ac.jp/crid/1360009142670793984","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Dimensional oxidization on coset space"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013168758878080","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"MacMahon KZ equation for Ding-Iohara-Miki algebra"}]},{"@id":"https://cir.nii.ac.jp/crid/1360017279843614464","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Elliptic quantum toroidal algebra $$U_{q,t,p}({\\mathfrak {gl}}_{1,tor})$$ and affine quiver gauge theories"}]},{"@id":"https://cir.nii.ac.jp/crid/1360017282422333824","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Gauge/Bethe correspondence from quiver BPS algebras"}]},{"@id":"https://cir.nii.ac.jp/crid/1360021389798043008","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360283690227305856","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Toric Calabi-Yau threefolds as quantum integrable systems. ℛ $$ \\mathrm{\\mathcal{R}} $$ -matrix and ℛ T T $$ \\mathrm{\\mathcal{R}}\\mathcal{T}\\mathcal{T} $$ relations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360285708898345856","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra, and 5D AGT correspondence"}]},{"@id":"https://cir.nii.ac.jp/crid/1360285709430717312","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Elliptic algebra, Frenkel–Kac construction and root of unity limit"}]},{"@id":"https://cir.nii.ac.jp/crid/1360290617647503744","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"q-deformation of corner vertex operator algebras by Miura transformation"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294643735591168","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Quasi-Hopf twist and elliptic Nekrasov factor"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294643773137536","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Toroidal and elliptic quiver BPS algebras and beyond"}]},{"@id":"https://cir.nii.ac.jp/crid/1360302866853887232","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"5d AGT correspondence of supergroup gauge theories from quantum toroidal $$ \\mathfrak{gl} $$1"}]},{"@id":"https://cir.nii.ac.jp/crid/1360306904409409920","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Elliptic deformation of the Gaiotto-Rapčák corner VOA and the associated partially symmetric polynoimals"}]},{"@id":"https://cir.nii.ac.jp/crid/1360565165203233408","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Explicit examples of DIM constraints for network matrix models"}]},{"@id":"https://cir.nii.ac.jp/crid/1360565165204352000","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"(p, q)-webs of DIM representations, 5d $$ \\mathcal{N}=1 $$ instanton partition functions and qq-characters"}]},{"@id":"https://cir.nii.ac.jp/crid/1360565165204600832","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver"}]},{"@id":"https://cir.nii.ac.jp/crid/1360565166054128768","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Anomaly in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:mi mathvariant=\"script\">RTT</mml:mi></mml:math> relation for DIM algebra and network matrix models"}]},{"@id":"https://cir.nii.ac.jp/crid/1360565169034882432","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Quantum toroidal gl1-algebra: Plane partitions"}]},{"@id":"https://cir.nii.ac.jp/crid/1360567181083301504","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"An elliptic vertex of Awata-Feigin-Shiraishi type for M-strings"}]},{"@id":"https://cir.nii.ac.jp/crid/1360567181125108992","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"A note on Bridgeland’s Hall algebra of two-periodic complexes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360567182187098752","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Representations of quantum toroidal<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msub><mml:mrow><mml:mi mathvariant=\"fraktur\">gl</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>"}]},{"@id":"https://cir.nii.ac.jp/crid/1360567184407463936","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Integrals of motion from quantum toroidal algebras"}]},{"@id":"https://cir.nii.ac.jp/crid/1360568465701685248","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Web construction of ABCDEFG and affine quiver gauge theories"}]},{"@id":"https://cir.nii.ac.jp/crid/1360568467127912832","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Can tangle calculus be applicable to hyperpolynomials?"}]},{"@id":"https://cir.nii.ac.jp/crid/1360572092539741568","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Free field approach to the Macdonald process"}]},{"@id":"https://cir.nii.ac.jp/crid/1360580232391945344","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Shifted quiver quantum toroidal algebra and subcrystal representations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360846640178764416","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Quantum algebraic approach to refined topological vertex"}]},{"@id":"https://cir.nii.ac.jp/crid/1360846642759261184","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848656053698304","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"(q, t)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848656055322240","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"The MacMahon R-matrix"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848656108679424","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Finite Type Modules and Bethe Ansatz for Quantum Toroidal \n\n$${\\mathfrak{gl}_1}$$\n                \n                    \n                                    \n                        \n                            gl\n                            1"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848656332978688","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Whittaker Vector of Deformed Virasoro Algebra and Macdonald Symmetric Functions"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848656333043456","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Kac determinant and singular vector of the level N representation of Ding–Iohara–Miki algebra"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848659384278784","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"An elliptic topological vertex"}]},{"@id":"https://cir.nii.ac.jp/crid/1360861707132406528","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"A note on quiver quantum toroidal algebra"}]},{"@id":"https://cir.nii.ac.jp/crid/1360865815486057600","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Quantum toroidal algebras and solvable structures in gauge/string theory"}]},{"@id":"https://cir.nii.ac.jp/crid/2050307417114067840","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"The Nambu bracket and M-theory"}]},{"@id":"https://cir.nii.ac.jp/crid/2050307417125028352","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"A note on the S-dual basis in the free fermion system"}]},{"@id":"https://cir.nii.ac.jp/crid/2050870367067511424","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Coherent states in quantum W1+∞ algebra and qq-character for 5d super Yang-Mills"}]},{"@id":"https://cir.nii.ac.jp/crid/2050870367068460032","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"The Maulik-Okounkov R-matrix from the Ding-Iohara-Miki algebra"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1063/1.2823979"},{"@type":"CROSSREF","@value":"10.1007/jhep08(2013)028_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1093/integr/xyx009_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1016/j.nuclphysb.2019.114816_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep08(2020)150_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep10(2020)198_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep04(2021)031_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/s11005-023-01650-6_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep11(2022)119_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/s10468-024-10251-3_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep10(2016)047_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1063/1.4993773_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1088/1751-8121/aa8233_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1215/21562261-1625217_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1016/j.jalgebra.2012.12.029_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep04(2021)202_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep12(2021)130_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep02(2022)024_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep12(2022)157_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep08(2024)233_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep07(2016)103_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep11(2017)034_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep12(2017)015_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep08(2018)050_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/s00209-015-1573-x_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1088/1751-8121/aa8e92_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1093/ptep/ptw075_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1093/ptep/ptw165_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep09(2019)025_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/s10801-020-00976-x_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep05(2022)122_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep03(2012)041_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1093/ptep/ptx123_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1103/physrevd.96.026021_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep03(2018)192_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep04(2019)097_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/s00220-017-2984-9_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/s11005-016-0821-2_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/s11005-018-1094-8_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1088/1751-8121/aae654_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1093/ptep/ptz158_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1016/j.nuclphysb.2017.03.003_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1007/jhep05(2022)011_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"},{"@type":"CROSSREF","@value":"10.1016/j.physrep.2023.12.003_references_DOI_9ncmzVBSncK0XfHzu442sSJwtTG"}]}