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How to sharpen a tridiagonal pair
https://doi.org/10.24517/00011037
https://doi.org/10.24517/00011037e5bea0db-0146-4745-a3d8-506e53b06ffe
| 名前 / ファイル | ライセンス | アクション |
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SC-PR-ITO-T-543.pdf (158.1 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 | How to sharpen a tridiagonal pair | |||||||
| 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 | 10.24517/00011037 | |||||||
| ID登録タイプ | JaLC | |||||||
| 著者 |
Ito, Tatsuro
× Ito, Tatsuro× Paul, Terwilliger |
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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 |
Journal of Algebra and its Applications 巻 9, 号 4, p. 543-552, 発行日 2010-08-01 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 0219-4988 | |||||||
| NCID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AA11646389 | |||||||
| DOI | ||||||||
| 関連タイプ | isVersionOf | |||||||
| 識別子タイプ | DOI | |||||||
| 関連識別子 | 10.1142/S0219498810004105 | |||||||
| 出版者 | ||||||||
| 出版者 | World Scientific Publishing | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | Let 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} di=0 of the eigenspaces of A such that A* V i ⊆ Vi-1 + Vi + Vi+1 for 0 ≤ i ≤ d, where V-1 = 0 and Vd+1 = 0; (iii) there exists an ordering {Vi*}δi=0 of the eigenspaces of A* such that AV*i ⊆V* i-1+V*i+V*i+1 for 0 ≤ i ≤ δ, where V*-1=0 and V*δ+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, V*i, Vd-i, V*d-i coincide. Denote this common dimension by ρi and call A, A* sharp whenever ρ0 = 1. Let T denote the -subalgebra of End (V) generated by A, A*. We show: (i) the center Z(T) is a field whose dimension over is ρ0; (ii) the field Z(T) is isomorphic to each of E 0TE0, EdTEd, E* 0TE*0, E*dTE*d, where Ei (resp. E*i) is the primitive idempotent of A (resp. A*) associated with Vi (resp. V*i); (iii) with respect to the Z(T)-vector space V the pair A, A* is a sharp tridiagonal pair. © 2010 World Scientific Publishing Company. | |||||||
| 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 | |||||||
