A Linear Map Acts as a Leonard Pair with Each of the Generators of

Hasan Alnajjar

International Journal of Mathematics and Mathematical Sciences, 2020, vol. 2020, 1-9

Abstract:

Let denote an algebraically closed field with a characteristic not two. Fix an integer ; let , , and be the equitable basis of over . Let denote an irreducible - module with dimension ; let . In this paper, we show that if each of the pairs , , and acts on as a Leonard pair, then these pairs are of Krawtchouk type. Moreover, is a linear combination of 1, , , and .

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:3593296

DOI: 10.1155/2020/3593296

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