Conformal blocks are extensively used as trial wave functions in the Quantum Hall Effect. The interpretation as wavefunctions implies that there is a scalar product on the space of relevant conformal blocks. Does this scalar product have any interpretation within the CFT framework, without reference to the Quantum Hall Effect?

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Addition: example for the sake of illustration and making the question more concrete. Conformal block is a function of $n$ points $B(z_1,\dots,z_n)$ which are interpreted as positions of particles in the QHE. Then for example the integral $\int d^2z_1\dots d^2z_n |B(z_1,\dots,z_n)|^2$ is a norm of the corresponding state. So, does this expression correspond to any known object in the original conformal field theory?