Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.

Comment on "Evidence for quantized displacement in macroscopic nanomechanical oscillators"

A Comment on the Letter by Alexei Gaidarzhy et al., Phys. Rev. Lett. 94, 030402 (2005). The authors of the Letter offer a Reply.

Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras

The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U-q (gl(m/n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U-q[osp(m/n)]. In this manner, we obtain generalizations of the Perk-Schultz model.