Tridiagonal pairs of Krawtchouk type
| dc.creator | Ito, Tatsuro | |
| dc.creator | Terwilliger, Paul | |
| dc.date | 2007-06-07 | |
| dc.date.accessioned | 2026-07-07T08:04:32Z | |
| dc.date.available | 2026-07-07T08:04:32Z | |
| dc.description | Let $K$ denote an algebraically closed field with characteristic 0 and let $V$ denote a vector space over $K$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$ with diameter $d$. We say that $A,A^*$ has Krawtchouk type whenever the sequence $\lbrace d-2i\rbrace_{i=0}^d$ is a standard ordering of the eigenvalues of $A$ and a standard ordering of the eigenvalues of $A^*$. Assume $A,A^*$ has Krawtchouk type. We show that there exists a nondegenerate symmetric bilinear form $< , >$ on $V$ such that $<Au,v>= < u,Av>$ and $<A^*u,v >= < u,A^*v>$ for $u,v\in V$. We show that the following tridiagonal pairs are isomorphic: (i) $A,A^*$; (ii) $-A,-A^*$; (iii) $A^*,A$; (iv) $-A^*,-A$. We give a number of related results and conjectures. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0706.1065 | |
| dc.identifier | http://arxiv.org/abs/0706.1065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129995 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.subject | 33C45; 05E30,15A21 | |
| dc.title | Tridiagonal pairs of Krawtchouk type | |
| dc.type | text |