Leonard pairs from 24 points of view
| dc.creator | Terwilliger, Paul | |
| dc.date | 2004-06-28 | |
| dc.date.accessioned | 2026-07-07T05:09:47Z | |
| dc.date.available | 2026-07-07T05:09:47Z | |
| dc.description | 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 $A:V\to V$ 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. We call such a pair a {\it Leonard pair} on $V$. Referring to the above Leonard pair, we investigate 24 bases for $V$ on which the action of $A$ and $A^*$ takes an attractive form. With respect to each of these bases, the matrices representing $A$ and $A^*$ are either diagonal, lower bidiagonal, upper bidiagonal, or tridiagonal. | |
| dc.description | 50 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0406577 | |
| dc.identifier | http://arxiv.org/abs/math/0406577 | |
| dc.identifier | Rocky Mountain J. Math. 32 (2002), 827--888 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71711 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Mathematical Physics | |
| dc.subject | 17B37; 05E30 | |
| dc.title | Leonard pairs from 24 points of view | |
| dc.type | text |