کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603498 1336962 2008 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Tridiagonal pairs of shape (1, 2, 1)
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Tridiagonal pairs of shape (1, 2, 1)
چکیده انگلیسی

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 satisfies the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering 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 of the eigenspaces of A∗ such that for 0⩽i⩽δ, where and ; (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 that for 0⩽i⩽d the dimensions of coincide; we denote this common value by ρi. The sequence is called the shape of the pair. In this paper we assume the shape is (1,2,1) and obtain the following results. We describe six bases for V; one diagonalizes A, another diagonalizes A∗, and the other four underlie the split decompositions for A,A∗. We give the action of A and A∗ on each basis. For each ordered pair of bases among the six, we give the transition matrix. At the end we classify the tridiagonal pairs of shape (1,2,1) in terms of a sequence of scalars called the parameter array.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issue 1, 1 July 2008, Pages 403-428