Degenerate Series Representations of the q-Deformed Algebra so'q(r,s)
The q-deformed algebra so'q(r,s) is a real form of the q-deformed algebra Uq'(so(n,C)), n = r + s, which differs from the quantum algebra Uq(so(n,C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so'q(r,s). The formulas of action of opera...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147377 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) / V.A. Groza // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862540396957007872 |
|---|---|
| author | Groza, V.A. |
| author_facet | Groza, V.A. |
| citation_txt | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) / V.A. Groza // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The q-deformed algebra so'q(r,s) is a real form of the q-deformed algebra Uq'(so(n,C)), n = r + s, which differs from the quantum algebra Uq(so(n,C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so'q(r,s). The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra so'q(r) × so'q(s) are given. Most of these representations are irreducible. Reducible representations appear under some conditions for the parameters determining the representations. All irreducible constituents which appear in reducible representations of the degenerate series are found. All *-representations of so'q(r,s) are separated in the set of irreducible representations obtained in the paper.
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| first_indexed | 2025-11-24T16:08:46Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147377 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T16:08:46Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Groza, V.A. 2019-02-14T14:53:02Z 2019-02-14T14:53:02Z 2007 Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) / V.A. Groza // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 16B35; 16B37; 81R50 https://nasplib.isofts.kiev.ua/handle/123456789/147377 The q-deformed algebra so'q(r,s) is a real form of the q-deformed algebra Uq'(so(n,C)), n = r + s, which differs from the quantum algebra Uq(so(n,C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so'q(r,s). The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra so'q(r) × so'q(s) are given. Most of these representations are irreducible. Reducible representations appear under some conditions for the parameters determining the representations. All irreducible constituents which appear in reducible representations of the degenerate series are found. All *-representations of so'q(r,s) are separated in the set of irreducible representations obtained in the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) Article published earlier |
| spellingShingle | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) Groza, V.A. |
| title | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) |
| title_full | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) |
| title_fullStr | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) |
| title_full_unstemmed | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) |
| title_short | Degenerate Series Representations of the q-Deformed Algebra so'q(r,s) |
| title_sort | degenerate series representations of the q-deformed algebra so'q(r,s) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147377 |
| work_keys_str_mv | AT grozava degenerateseriesrepresentationsoftheqdeformedalgebrasoqrs |