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Tridiagonal pairs of q-Racah type
https://doi.org/10.24517/00011038
https://doi.org/10.24517/000110383619cf82-9f66-43b4-9315-730f34b4f6bb
| 名前 / ファイル | ライセンス | アクション |
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SC-PR-ITO-T-68.pdf (185.7 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 | Tridiagonal pairs of q-Racah type | |||||||
| 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 | 10.24517/00011038 | |||||||
| 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 巻 322, 号 1, p. 68-93, 発行日 2009-07-01 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 0021-8693 | |||||||
| NCID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AA00692420 | |||||||
| DOI | ||||||||
| 関連タイプ | isVersionOf | |||||||
| 識別子タイプ | DOI | |||||||
| 関連識別子 | 10.1016/j.jalgebra.2009.04.008 | |||||||
| 出版者 | ||||||||
| 出版者 | Academic Press | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | Let F denote an algebraically closed 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 A Vi* ⊆ 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 A W ⊆ W, A* W ⊆ W, W ≠ 0, W ≠ V. We call such a pair a tridiagonal pair on V. It is known that d = δ. For 0 ≤ i ≤ d let θi (resp. θi*) denote the eigenvalue of A (resp. A*) associated with Vi (resp. Vi*). The pair A, A* is said to have q-Racah type whenever θi = a + b q2 i - d + c qd - 2 i and θi* = a* + b* q2 i - d + c* qd - 2 i for 0 ≤ i ≤ d, where q, a, b, c, a*, b*, c* are scalars in F with q, b, c, b*, c* nonzero and q2 ∉ {1, - 1}. This type is the most general one. We classify up to isomorphism the tridiagonal pairs over F that have q-Racah type. Our proof involves the representation theory of the quantum affine algebra Uq (over(sl, ̂)2). © 2009 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 | |||||||
