  Recently, it has been proposed that the dimension of the Hilbert space of
quantum gravity in deSitter space is finite and moreover it is expressed in
terms of the coupling constants by using the entropy formula. A weaker
conjecture would be that the coupling constant in deSitter space should take
only discrete values not necessarily given by the entropy formula. We discuss
quantization of the horizon in deSitter space by using Berezin's functorial
quantization of Kahler manifolds and argue that the weak conjecture is valid
for Euclidean deSitter space. Moreover it can be valid for a class of bounded
complex symmetric spaces.
