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ファイル | 記述 | サイズ | フォーマット | |
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ajm.2017.0015.pdf | 298.72 kB | Adobe PDF | 見る/開く |
タイトル: | An algebraic study of extension algebras |
著者: | Kato, Syu |
著者名の別形: | 加藤, 周 |
発行日: | Jun-2017 |
出版者: | Johns Hopkins University Press |
誌名: | American Journal of Mathematics |
巻: | 139 |
号: | 3 |
開始ページ: | 567 |
終了ページ: | 615 |
抄録: | We present simple conditions which guarantee a geometric extension algebra to behave like a variant of quasi-hereditary algebras. In particular, standard modules of affine Hecke algebras of type $sf{BC}$, and the quiver Schur algebras are shown to satisfy the Brauer-Humphreys type reciprocity and the semi-orthogonality property. In addition, we present a new criterion of purity of weights in the geometric side. This yields a proof of Shoji's conjecture on limit symbols of type $sf{B}$ [T. Shoji, {it Adv. Stud. Pure Math.} 40 (2004)], and the purity of the exotic Springer fibers [S. Kato, {it Duke Math. J.} 148 (2009)]. Using this, we describe the leading terms of the $C^{infty}$-realization of a solution of the Lieb-McGuire system in the appendix. In [S. Kato, {it Duke Math. J.} 163 (2014)], we apply the results of this paper to the KLR algebras of type $sf{ADE}$ to establish Kashwara's problem and Lusztig's conjecture. |
著作権等: | This article appeared in the American Journal of Mathematics, Volume 139, Issue 3, 2017, pages 576-615, Copyright © 2017, Johns Hopkins 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。 |
URI: | http://hdl.handle.net/2433/230135 |
DOI(出版社版): | 10.1353/ajm.2017.0015 |
関連リンク: | https://muse.jhu.edu/article/657763/summary |
出現コレクション: | 学術雑誌掲載論文等 |
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