On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra
In [Kyushu J. Math. 64 (2010), 81-144], it is discussed that a certain subalgebra of the quantum affine algebra Uq(sl₂) controls the second kind TD-algebra of type I (the degenerate q-Onsager algebra). The subalgebra, which we denote by U'q(sl₂), is generated by e+0, e±₁, k±¹ i (i=0,1) with e−0...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
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Інститут математики НАН України
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146905 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra / T. Hattai, T. Ito // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734090722082816 |
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| author | Hattai, T. Ito, T. |
| author_facet | Hattai, T. Ito, T. |
| citation_txt | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra / T. Hattai, T. Ito // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In [Kyushu J. Math. 64 (2010), 81-144], it is discussed that a certain subalgebra of the quantum affine algebra Uq(sl₂) controls the second kind TD-algebra of type I (the degenerate q-Onsager algebra). The subalgebra, which we denote by U'q(sl₂), is generated by e+0, e±₁, k±¹ i (i=0,1) with e−0 missing from the Chevalley generators e±i, k±¹i (i=0,1) of Uq(sl₂). In this paper, we determine the finite-dimensional irreducible representations of U′q(sl₂). Intertwiners are also determined.
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| first_indexed | 2025-12-07T19:40:39Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146905 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:40:39Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
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| spelling | Hattai, T. Ito, T. 2019-02-11T21:27:36Z 2019-02-11T21:27:36Z 2015 On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra / T. Hattai, T. Ito // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 5 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B37; 05E30 DOI:10.3842/SIGMA.2015.007 https://nasplib.isofts.kiev.ua/handle/123456789/146905 In [Kyushu J. Math. 64 (2010), 81-144], it is discussed that a certain subalgebra of the quantum affine algebra Uq(sl₂) controls the second kind TD-algebra of type I (the degenerate q-Onsager algebra). The subalgebra, which we denote by U'q(sl₂), is generated by e+0, e±₁, k±¹ i (i=0,1) with e−0 missing from the Chevalley generators e±i, k±¹i (i=0,1) of Uq(sl₂). In this paper, we determine the finite-dimensional irreducible representations of U′q(sl₂). Intertwiners are also determined. This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
 available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
 The research of the second author is supported by Science Foundation of Anhui University
 (Grant No. J10117700037). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra Article published earlier |
| spellingShingle | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra Hattai, T. Ito, T. |
| title | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra |
| title_full | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra |
| title_fullStr | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra |
| title_full_unstemmed | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra |
| title_short | On a Certain Subalgebra of Uq(sl₂) Related to the Degenerate q-Onsager Algebra |
| title_sort | on a certain subalgebra of uq(sl₂) related to the degenerate q-onsager algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146905 |
| work_keys_str_mv | AT hattait onacertainsubalgebraofuqsl2relatedtothedegenerateqonsageralgebra AT itot onacertainsubalgebraofuqsl2relatedtothedegenerateqonsageralgebra |