A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra
We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(gln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weig...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146061 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra / M.J. Hopkins, A.I. Molev // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716249519161344 |
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| author | Hopkins, M.J. Molev, A.I. |
| author_facet | Hopkins, M.J. Molev, A.I. |
| citation_txt | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra / M.J. Hopkins, A.I. Molev // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(gln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand-Tsetlin character (or q-character). We also apply the quantum Sylvester theorem to construct a q-analogue of the Olshanski algebra as a projective limit of certain centralizers in Uq(gln) and show that this limit algebra contains the q-Yangian as a subalgebra.
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| first_indexed | 2025-12-07T18:03:46Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146061 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:03:46Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hopkins, M.J. Molev, A.I. 2019-02-06T16:48:55Z 2019-02-06T16:48:55Z 2006 A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra / M.J. Hopkins, A.I. Molev // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R10 https://nasplib.isofts.kiev.ua/handle/123456789/146061 We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(gln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand-Tsetlin character (or q-character). We also apply the quantum Sylvester theorem to construct a q-analogue of the Olshanski algebra as a projective limit of certain centralizers in Uq(gln) and show that this limit algebra contains the q-Yangian as a subalgebra. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. We would like to thank Boris Feigin for discussions and Serge Ovsienko for help with the proof
 of Theorem 5.4. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra Article published earlier |
| spellingShingle | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra Hopkins, M.J. Molev, A.I. |
| title | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra |
| title_full | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra |
| title_fullStr | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra |
| title_full_unstemmed | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra |
| title_short | A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra |
| title_sort | q-analogue of the centralizer construction and skew representations of the quantum affine algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146061 |
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