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A classification of sharp tridiagonal pairs
https://doi.org/10.24517/00010387
https://doi.org/10.24517/00010387948a01b2-a21e-430c-b749-48fddcf02394
| 名前 / ファイル | ライセンス | アクション |
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SC-PR-ITO-T-1857.pdf (307.2 kB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||||
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| 公開日 | 2017-10-03 | |||||||
| タイトル | ||||||||
| タイトル | A classification of sharp tridiagonal pairs | |||||||
| 言語 | en | |||||||
| 言語 | ||||||||
| 言語 | eng | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | journal article | |||||||
| ID登録 | ||||||||
| ID登録 | 10.24517/00010387 | |||||||
| ID登録タイプ | JaLC | |||||||
| 著者 |
Ito, Tatsuro
× Ito, Tatsuro× Nomura, Kazumasa× Terwilligerc, Paul |
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| 著者別表示 |
伊藤, 達郎
× 伊藤, 達郎
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| 提供者所属 | ||||||||
| 内容記述タイプ | Other | |||||||
| 内容記述 | 金沢大学理工研究域数物科学系 | |||||||
| 書誌情報 |
Linear Algebra and Its Applications 巻 435, 号 8, p. 1857-1884, 発行日 2011-10-15 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 0024-3795 | |||||||
| NCID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AA00717292 | |||||||
| 出版者 | ||||||||
| 出版者 | Elsevier | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A : V → V and A* : V → V that satisfy the following conditions: (i) each of A, A* is diagonalizable; (ii) there exists an ordering {Vi}i = 0d of the eigenspaces of A such that A* Vi ⊆ Vi - 1 + Vi + Vi + 1 for 0 ≤ i ≤ d, where V- 1 = 0 and Vd + 1 = 0; (iii) there exists an ordering {Vi*}i = 0δ of the eigenspaces of A* such that AVi* ⊆ Vi - 1* + Vi* + Vi + 1* for 0 ≤ i ≤ δ, where V- 1* = 0 and Vδ + 1* = 0; (iv) there is no subspace W of V such that AW ⊆ W, A* W ⊆ W, W ≠ 0, W ≠ V. We call such a pair a tridiagonal pair on V. It is known that d = δ and for 0 ≤ i ≤ d the dimensions of Vi, Vd - i, Vi*, Vd - i* coincide. The pair A, A* is called sharp whenever dim V0 = 1. It is known that if F is algebraically closed then A, A* is sharp. In this paper we classify up to isomorphism the sharp tridiagonal pairs. As a corollary, we classify up to isomorphism the tridiagonal pairs over an algebraically closed field. We obtain these classifications by proving the μ-conjecture. © 2011 Elsevier Inc. All rights reserved. | |||||||
| 著者版フラグ | ||||||||
| 出版タイプ | AM | |||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||
| 関連URI | ||||||||
| 関連タイプ | isIdenticalTo | |||||||
| 識別子タイプ | URI | |||||||
| 関連識別子 | http://www.elsevier.com/locate/issn/00243795 | |||||||
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| 関連タイプ | isVersionOf | |||||||
| 識別子タイプ | DOI | |||||||
| 関連識別子 | https://doi.org/10.1016/j.laa.2011.03.032 | |||||||
