Central elements of the elliptic $Z_n$ monodromy matrix algebra at roots of unity

Details Central elements of the elliptic $Z_n$ monodromy matrix algebra at roots of unity Central elements of the elliptic $Z_n$ monodromy matrix algebra at roots of unity

2004-04-13

arxiv.org/abs/hep-th/0404089v2

Nucl.Phys. B710 (2005) 614-628

Physics

High Energy Physics

High Energy Physics - Theory

Latex file, 18 pages; V2: minor typos corrected and a reference updated

Scientific paper

10.1016/j.nuclphysb.2004.12.033

The central elements of the algebra of monodromy matrices associated with the $\mathbb{Z}_n$ R-matrix are studied. When the crossing parameter $w$ takes a special rational value $w=\frac{n}{N}$, 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.

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