In geometric quantization, the quantum Hilbert space depends not only on the symplectic manifold, but on additional data such as the prequantum line bundle and polarization. These Hilbert spaces can be identified if there is a projectively flat connection on the space of polarizations considered. A well-known example is the quantization of the ChernSimons gauge theory, in which case there is a projectively flat connection on the moduli space of complex structures on a Riemann surface. In this talk, we discuss the projective flatness in geometric quantization, especially when the symplectic manifold is a linear space.