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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| Datum: | 2006 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2006
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146061 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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irk-123456789-1460612019-02-07T01:24:10Z A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra Hopkins, M.J. Molev, A.I. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146061 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Hopkins, M.J. Molev, A.I. |
| spellingShingle |
Hopkins, M.J. Molev, A.I. A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hopkins, M.J. Molev, A.I. |
| author_sort |
Hopkins, M.J. |
| title |
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_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_sort |
q-analogue of the centralizer construction and skew representations of the quantum affine algebra |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146061 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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