Quantization of moduli spaces of flat connections andconformal field theory

The known relations between quantised moduli spaces of flat connections on Riemannsurfaces and conformal field theory (CFT) have interesting generalisations to cases correspondingto non-compact groups. The relevant conformal field theories like the Liouvilleor Toda field theories will then have continuous spectra. The conformal blocksof the Liouville theory can be characterised as solutions of a Riemann-Hilbert problemnaturally arising in the quantisation of the moduli spaces of flat connections