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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2006 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146061 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146061 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra |
| spellingShingle |
A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra Hopkins, M.J. Molev, A.I. |
| 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 |
| author |
Hopkins, M.J. Molev, A.I. |
| author_facet |
Hopkins, M.J. Molev, A.I. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
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