کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416397 | 1631140 | 2014 | 21 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Leonard pairs having LB-TD form Leonard pairs having LB-TD form](/preview/png/6416397.png)
Fix an algebraically closed field F and an integer dâ¥3. Let Matd+1(F) denote the F-algebra consisting of the (d+1)Ã(d+1) matrices that have all entries in F. We consider a pair of diagonalizable matrices A,Aâ in Matd+1(F), each acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. Such a pair is called a Leonard pair in Matd+1(F). For a Leonard pair A,Aâ there is a nonzero scalar q that is used to describe the eigenvalues of A and Aâ. In the present paper we find all Leonard pairs A,Aâ in Matd+1(F) such that A is lower bidiagonal with subdiagonal entries all 1 and Aâ is irreducible tridiagonal, under the assumption that q is not a root of unity. This gives a partial solution of a problem given by Paul Terwilliger.
Journal: Linear Algebra and its Applications - Volume 455, 15 August 2014, Pages 1-21