Generalized chiral Potts models and minimal cyclic representations of $$ {U_q}(\widehat {\mathfrak{g}\mathfrak{l}}(n,C))$$

Abstract

Finite-dimensional cyclic representations of the quantized universal enveloping algebra U q (g) exist only when the deformation parameter q is a root of unity, q N = 1. In such representations, the N-th power of each Chevalley generator acts as a non-zero scalar. These values of e i N , f i/ N and t i N are part of a continuous family of parameters upon which the cyclic representations depend.