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 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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. |
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