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Title: Poincaré–Birkhoff–Witt bases and Khovanov–Lauda–Rouquier algebras
Authors: Kato, Syu
Author's alias: 加藤, 周
Issue Date: Feb-2014
Publisher: Duke University Press
Journal title: Duke Mathematical Journal
Volume: 163
Issue: 3
Start page: 619
End page: 663
Abstract: We 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.
Rights: ©2014 Duke University Press
This 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。
DOI(Published Version): 10.1215/00127094-2405388
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