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Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations
Інший ID:
2000 Mathematics Subject Classification: 33D15; 81R50; 82B23
Посилання:
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.
Підтримка:
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.
Дата:
2006
Переглядів:
615
Завантажень:
279
Анотація:
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.
