Some algebra related to P- and Q-polynomial association schemes
Abstrak
Let $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. Consider a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ 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.
Topik & Kata Kunci
Penulis (3)
Tatsuro Ito
K. Tanabe
Paul M. Terwilliger
Akses Cepat
- Tahun Terbit
- 2001
- Bahasa
- en
- Total Sitasi
- 220×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1090/dimacs/056/14
- Akses
- Open Access ✓