The centre of the graph and moduli algebras at roots of 1

Details The centre of the graph and moduli algebras at roots of 1 The centre of the graph and moduli algebras at roots of 1

1996-02-29

arxiv.org/abs/q-alg/9602036v1

Commun.Math.Phys. 200 (1999) 599-619

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, latex, no figures

Scientific paper

10.1007/s002200050542

The structure of the centres ${\cal Z}(\Lg)$ and ${\cal Z}(\Mg)$ of the graph algebra ${\cal L}_g(sl_2)$ and the moduli algebra ${\cal M}_g(sl_2)$ is studied at roots of 1. It it shown that ${\cal Z}(\Lg)$ can be endowed with the structure of the Poisson graph algebra. The elements of $Spec({\cal Z}(\Mg))$ are shown to satisfy the defining relation for the holonomies of a flat connection along the cycles of a Riemann surface. The irreducible representations of the graph algebra are constructed.

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