Dynamical R matrices of elliptic quantum groups and connection matrices for the q-KZ equations

• Дата: 2006
• Автор: Konno, H.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2006
• Назва видання: Symmetry, Integrability and Geometry: Methods and Applications
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/146062
• 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.

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.