A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2
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...
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Hindawi Limited
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/3593296 |
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doaj-42a8f715294749cc99ecd5b2340c225c2020-11-25T01:25:41ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/35932963593296A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2Hasan Alnajjar0Department of Mathematics, The University of Jordan, Amman 11942, JordanLet 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.http://dx.doi.org/10.1155/2020/3593296 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hasan Alnajjar |
| spellingShingle |
Hasan Alnajjar A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2 International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Hasan Alnajjar |
| author_sort |
Hasan Alnajjar |
| title |
A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2 |
| title_short |
A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2 |
| title_full |
A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2 |
| title_fullStr |
A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2 |
| title_full_unstemmed |
A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2 |
| title_sort |
linear map acts as a leonard pair with each of the generators of usl2 |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2020-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2020/3593296 |
| work_keys_str_mv |
AT hasanalnajjar alinearmapactsasaleonardpairwitheachofthegeneratorsofusl2 AT hasanalnajjar linearmapactsasaleonardpairwitheachofthegeneratorsofusl2 |
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