2005/08/22 by Kazumasa Nomura, Paul Terwilliger, Nomura, Kazumasa +1 · 2 citations
Computer Science · Engineering · Mathematics · #05E35 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.CO #math.RA #msc:05E35
paper · pdf · doi:10.48550/arxiv.math/0508407
13 pages
arxiv created 2005/08/22 · openalex publication_date 2005/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A:V → V and A^*:V → V that satisfy (i), (ii) below: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A^* is diagonal. (ii) There exists a basis for V with respect to which the matrix representing A^* is irreducible tridiagonal and the matrix representing A is diagonal. We call such a pair a \em Leonard pair on V. In the literature on Leonard pairs there exist two parameter sequences called the first split sequence and the second split sequence. We display some attractive formulae for the first and second split sequence that involve the trace function.