The quantisation of poisson structures arising in chern-simons theory with gauge group G ⋉g

We quantise a Poisson structure on H^n+2g, where H is a semidirect product group of the form G × g*. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group G ? g* on R × S_g,n, where S_g,n is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with gauge group G × g*. We construct the quantum algebra and its irreducible representations and show that the quantum double D(G) of the group G arises naturally as a symmetry of the quantum algebra. © 2002 International Press.