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dc.contributor.authorKato, Syuja
dc.contributor.alternative加藤, 周ja
dc.date.accessioned2014-05-19T04:24:44Z-
dc.date.available2014-05-19T04:24:44Z-
dc.date.issued2014-02ja
dc.identifier.issn0012-7094ja
dc.identifier.urihttp://hdl.handle.net/2433/187073-
dc.description.abstractWe generalize Lusztig’s geometric construction of the Poincaré–Birkhoff–Witt (PBW) bases of finite quantum groups of type ADE under the framework of Varagnolo and Vasserot. In particular, every PBW basis of such quantum groups is proven to yield a semi-orthogonal collection in the module category of the Khovanov–Lauda–Rouquier (KLR) algebras. This enables us to prove Lusztig’s conjecture on the positivity of the canonical (lower global) bases in terms of the (lower) PBW bases. In addition, we verify Kashiwara’s problem on the finiteness of the global dimensions of the KLR algebras of type ADE.ja
dc.format.mimetypeapplication/pdfja
dc.language.isoengja
dc.publisherDuke University Pressja
dc.rights©2014 Duke University Pressja
dc.rightsThis is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。ja
dc.titlePoincaré–Birkhoff–Witt bases and Khovanov–Lauda–Rouquier algebrasja
dc.type.niitypeJournal Articleja
dc.identifier.ncidAA00630478ja
dc.identifier.jtitleDuke Mathematical Journalja
dc.identifier.volume163ja
dc.identifier.issue3ja
dc.identifier.spage619ja
dc.identifier.epage663ja
dc.relation.doi10.1215/00127094-2405388ja
dc.textversionauthorja
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