2004/06/27 by Tatsuro Ito, Kenichiro Tanabe, Paul Terwilliger · 1 citation
Mathematics · #math.CO #math.QA #msc:05E30 #msc:17B37
published as Proceedings of DIMACS conference on Codes and Association Schemes, (Piscataway NJ, 1999), 167--192. Amer. Math. Soc. Providence RI, 2001 · 26 pages
arxiv created 2004/06/27 · arxiv updated 2009/12/01
Let K denote a field, and let V denote a vector space over K with finite positive dimension. Consider a pair of linear transformations A:V→ V and A^*:V→ V that satisfy both conditions below: (i) There exists a basis for V with respect to which the matrix representing A is diagonal, and the matrix representing A^* is irreducible tridiagonal. (ii) There exists a basis for V with respect to which the matrix representing A^* is diagonal, and the matrix representing A is irreducible tridiagonal. Such a pair is called a Leonard pair on V. In this paper we introduce a mild generalization of a Leonard pair called a tridiagonal pair. A Leonard pair is the same thing as a tridiagonal pair such that for each transformation all eigenspaces have dimension one.