A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2
2020 ◽
Vol 2020
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pp. 1-9
Keyword(s):
Let ℱ denote an algebraically closed field with a characteristic not two. Fix an integer d≥3; let x, y, and z be the equitable basis of sl2 over ℱ. Let V denote an irreducible sl2-module with dimension d+1; let A∈EndV. In this paper, we show that if each of the pairs A,x, A,y, and A,z acts on V as a Leonard pair, then these pairs are of Krawtchouk type. Moreover, A is a linear combination of 1, x, y, and z.
Keyword(s):
1959 ◽
Vol 14
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pp. 223-234
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Keyword(s):
2013 ◽
Vol 89
(2)
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pp. 234-242
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2014 ◽
Vol 35
(7)
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pp. 2242-2268
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2011 ◽
Vol 11
(2)
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pp. 221-271
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1976 ◽
Vol 59
(1)
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pp. 29-29
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Keyword(s):
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2008 ◽
Vol 4
(1)
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pp. 91-100
1968 ◽
Vol 9
(2)
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pp. 146-151
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