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Tridiagonal pairs of Krawtchouk type
- フォーマット:
- 論文
- 責任表示:
- Ito, Tatsuro ; Terwilliger, Paul
- 言語:
- 英語
- 出版情報:
- Elsevier, 2007-12-01
- 著者名:
- 掲載情報:
- Linear Algebra and Its Applications
- ISSN:
- 0024-3795
- 巻:
- 427
- 通号:
- 2-3
- 開始ページ:
- 218
- 終了ページ:
- 233
- バージョン:
- author
- 概要:
- 金沢大学大学院自然科学研究科計算科学<br />Let F denote an algebraically closed field with characteristic 0 and let V denote a vector space over F with finite positive dimension. Let A, A* denote a tridiagonal pair on V with diameter d. We say that A, A … * has Krawtchouk type whenever the sequence {d - 2 i}i = 0d is a standard ordering of the eigenvalues of A and a standard ordering of the eigenvalues of A*. Assume A, A* has Krawtchouk type. We show that there exists a nondegenerate symmetric bilinear form 〈, 〉 on V such that 〈 Au, v 〉 = 〈 u, Av 〉 and 〈 A* u, v 〉 = 〈 u, A* v 〉 for u, v ∈ V. We show that the following tridiagonal pairs are isomorphic: (i) A, A*; (ii) - A, - A*; (iii) A*, A; (iv) - A*, - A. We give a number of related results and conjectures. © 2007 Elsevier Inc. All rights reserved. 続きを見る
- URL:
- http://hdl.handle.net/2297/7381
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