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Leonard pairs having zero-diagonal TD-TD form | | Kazumasa Nomura
; | | Date: |
18 Mar 2015 | | Abstract: | Fix an algebraically closed field $mathbb{F}$ and an integer $n geq 1$. Let
$ ext{Mat}_n(mathbb{F})$ denote the $mathbb{F}$-algebra consisting of the $n
imes n$ matrices that have all entries in $mathbb{F}$. We consider a pair of
diagonalizable matrices in $ ext{Mat}_{n}(mathbb{F})$, each acting in an
irreducible tridiagonal fashion on an eigenbasis for the other one. Such a pair
is called a Leonard pair in $ ext{Mat}_{n}(mathbb{F})$. In the present paper,
we find all Leonard pairs $A,A^*$ in $ ext{Mat}_{n}(mathbb{F})$ such that
each of $A$ and $A^*$ is irreducible tridiagonal with all diagonal entries $0$.
This solves a problem given by Paul Terwilliger. | | Source: | arXiv, 1503.5262 | | Services: | Forum | Review | PDF | Favorites | |
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