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Title: An algebraic study of extension algebras
Authors: Kato, Syu
Author's alias: 加藤, 周
Issue Date: Jun-2017
Publisher: Johns Hopkins University Press
Journal title: American Journal of Mathematics
Volume: 139
Issue: 3
Start page: 567
End page: 615
Abstract: 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.
Rights: 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。
DOI(Published Version): 10.1353/ajm.2017.0015
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