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タイトル: A classification of sharp tridiagonal pairs
著者: Ito, Tatsuro link image
Nomura, Kazumasa
Terwilliger, Paul
伊藤, 達郎
発行日: 2011年11月15日
出版社(者): Elsevier B.V.
雑誌名: Linear Algebra and Its Applications
ISSN: 0024-3795
巻: 435
号: 8
開始ページ: 1857
終了ページ: 1884
キーワード: Leonard pair
q-Racah polynomials
Tridiagonal pair
抄録: 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 AVi⊆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, AW⊆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 dimV0=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.
DOI: 10.1016/j.laa.2011.03.032
URI: http://hdl.handle.net/2297/28547
関連URI: http://www.elsevier.com/locate/issn/00243795
資料種別: Journal Article
版表示: author

このアイテムを引用あるいはリンクする場合は次の識別子を使用してください。 http://hdl.handle.net/2297/28547



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