Quantization of 2+1 gravity for genus 2

In previous papers we established and discussed the algebra of observables for 2+1 gravity at both the classical and quantum levels, and gave a systematic discussion of the reduction of the expected number of independent observables to 6g-6 (g>1). In this paper the algebra of observables for the case g=2 is reduced to a very simple form. A Hilbert space of state vectors is defined and its representations are discussed using a deformation of the Euler {Γ} function. The deformation parameter {θ} depends on the cosmological and Planck's constants.