Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space
We realize the Hopf algebra Uq(sp₂n) as an algebra of quantum differential operators on the quantum symplectic space X(fs;R) and prove that X(fs;R) is a Uq(sp₂n)-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root ve...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149279 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space / J. Zhang, N. Hu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862548640127516672 |
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| author | Zhang, J. Hu, N. |
| author_facet | Zhang, J. Hu, N. |
| citation_txt | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space / J. Zhang, N. Hu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We realize the Hopf algebra Uq(sp₂n) as an algebra of quantum differential operators on the quantum symplectic space X(fs;R) and prove that X(fs;R) is a Uq(sp₂n)-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig's braid automorphisms of Uq(sp₂n).
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| first_indexed | 2025-11-25T18:56:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149279 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T18:56:17Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zhang, J. Hu, N. 2019-02-19T19:45:56Z 2019-02-19T19:45:56Z 2017 Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space / J. Zhang, N. Hu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B10; 17B37; 20G42; 81R50; 81R60; 81T75 DOI:10.3842/SIGMA.2017.084 https://nasplib.isofts.kiev.ua/handle/123456789/149279 We realize the Hopf algebra Uq(sp₂n) as an algebra of quantum differential operators on the quantum symplectic space X(fs;R) and prove that X(fs;R) is a Uq(sp₂n)-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig's braid automorphisms of Uq(sp₂n). The authors would appreciate the referees for their useful comments and good suggestions for
 improving the paper. The first author is supported by the NSFC (Grants No. 11101258 and
 No. 11371238). The second author is supported by the NSFC (Grant No. 11771142). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space Article published earlier |
| spellingShingle | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space Zhang, J. Hu, N. |
| title | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space |
| title_full | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space |
| title_fullStr | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space |
| title_full_unstemmed | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space |
| title_short | Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space |
| title_sort | realization of uq(sp₂n) within the differential algebra on quantum symplectic space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149279 |
| work_keys_str_mv | AT zhangj realizationofuqsp2nwithinthedifferentialalgebraonquantumsymplecticspace AT hun realizationofuqsp2nwithinthedifferentialalgebraonquantumsymplecticspace |