Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations
For any affine Lie algebra g, we show that any finite dimensional representation of the universal dynamical R matrix R(λ) of the elliptic quantum group Bq,λ(g) coincides with a corresponding connection matrix for the solutions of the q-KZ equation associated with Uq(g). This provides a general conne...
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| Дата: | 2006 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations / H. Konno // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 38 назв. — англ. |
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oai:nasplib.isofts.kiev.ua:123456789-1460622025-02-23T17:24:55Z Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations Konno, H. For any affine Lie algebra g, we show that any finite dimensional representation of the universal dynamical R matrix R(λ) of the elliptic quantum group Bq,λ(g) coincides with a corresponding connection matrix for the solutions of the q-KZ equation associated with Uq(g). This provides a general connection between Bq,l(g) and the elliptic face (IRF or SOS) models. In particular, we construct vector representations of R(λ) for g = An⁽¹⁾, Bn⁽¹⁾, Cn⁽¹⁾, Dn⁽¹⁾, and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We hence confirm the conjecture by Frenkel and Reshetikhin. This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). The author would like to thank Michio Jimbo and Masato Okado for stimulating discussions and valuable suggestions. He also thanks Atsuo Kuniba and Atsushi Nakayashiki for discussions. He is also grateful to the organizers of O’Raifeartaigh Symposium, Janos Balog, Laszlo Feher and Zalan Horvath, for their kind invitation and hospitality during his stay in Budapest. 2006 Article Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations / H. Konno // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 38 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33D15; 81R50; 82B23 https://nasplib.isofts.kiev.ua/handle/123456789/146062 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
For any affine Lie algebra g, we show that any finite dimensional representation of the universal dynamical R matrix R(λ) of the elliptic quantum group Bq,λ(g) coincides with a corresponding connection matrix for the solutions of the q-KZ equation associated with Uq(g). This provides a general connection between Bq,l(g) and the elliptic face (IRF or SOS) models. In particular, we construct vector representations of R(λ) for g = An⁽¹⁾, Bn⁽¹⁾, Cn⁽¹⁾, Dn⁽¹⁾, and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We hence confirm the conjecture by Frenkel and Reshetikhin. |
| format |
Article |
| author |
Konno, H. |
| spellingShingle |
Konno, H. Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Konno, H. |
| author_sort |
Konno, H. |
| title |
Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations |
| title_short |
Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations |
| title_full |
Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations |
| title_fullStr |
Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations |
| title_full_unstemmed |
Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations |
| title_sort |
dynamical r matrices of elliptic quantum groups and connection matrices for the q-kz equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| citation_txt |
Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations / H. Konno // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 38 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT konnoh dynamicalrmatricesofellipticquantumgroupsandconnectionmatricesfortheqkzequations |
| first_indexed |
2025-07-22T04:17:05Z |
| last_indexed |
2025-07-22T04:17:05Z |
| _version_ |
1838319220113276928 |