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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| Datum: | 2006 |
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| 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/123456789/146062 |
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| Zitieren: | 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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irk-123456789-1460622019-02-07T01:24:12Z 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. 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 http://dspace.nbuv.gov.ua/handle/123456789/146062 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 |
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 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146062 |
| 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 |
2025-07-10T23:04:45Z |
| last_indexed |
2025-07-10T23:04:45Z |
| _version_ |
1837303004130181120 |