کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4599285 | 1631128 | 2015 | 24 صفحه PDF | دانلود رایگان |
Let KK denote an algebraically closed field of characteristic zero. Let V denote a vector space over KK with finite positive dimension. By a Leonard triple on V we mean an ordered triple of linear transformations A , A⁎A⁎, AεAε in End(V)End(V) such that for each B∈{A,A⁎,Aε}B∈{A,A⁎,Aε} there exists a basis for V with respect to which the matrix representing B is diagonal and the matrices representing the other two linear transformations are irreducible tridiagonal. In this paper, we define a family of Leonard triples said to have classical type and show that these Leonard triples consist of two families: the Racah type and the Krawtchouk type. Moreover, we construct all Leonard triples that have classical type from the universal enveloping algebra U(sl2)U(sl2).
Journal: Linear Algebra and its Applications - Volume 467, 15 February 2015, Pages 202–225