Quantised affine algebras and parameter-dependent R-matrices

Abstract

Let Uq(G(1)) be a quantised non-twisted affine Lie algebra with Uq(G) the corresponding quantised simple Lie algebra. Using the previously obtained universal R-matrices for and , explicitly spectral-dependent universal R-matrices for Uq(A1) and Uq(A2) are determined. These spectral-dependent universal R-matrices are evaluated in some concrete representations; well-known results for the fundamental representations are reproduced, and an explicit formula for the spectral-dependent R-matrix associated with the V(3) ⊗ V(6) module is derived, where V(3) and V(6) carry the 3- and 6-dimensional representations of Uq(A2), respectively.