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SIGMA 2 (2006), 091, 25 pages math.QA/0612558
https://doi.org/10.3842/SIGMA.2006.091
Contribution to the Proceedings of the O'Raifeartaigh Symposium
Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
Hitoshi Konno
Department of Mathematics, Graduate School of Science,
Hiroshima University, Higashi-Hiroshima 739-8521, Japan
Received October 02, 2006, in final form November 28, 2006; Published online December 19, 2006
Abstract
For any affine Lie algebra g, we show that any
finite dimensional representation of the universal dynamical R
matrix R(l) of the elliptic quantum group
Bq,l(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(l) 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.
Key words:
elliptic quantum group; quasi-Hopf algebra.
pdf (393 kb)
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