Quantization of the space of conformal blocks

We consider the discrete Knizhnik-Zamolodchikov connection (qKZ) associated to gl(N), defined in terms of rational R-matrices. We prove that under certain resonance conditions, the qKZ connection has a non-trivial invariant subbundle which we call the subbundle of quantized conformal blocks. The subbundle is given explicitly by algebraic equations in terms of the Yangian Y(gl(N)) action. The subbundle is a deformation of the subbundle of conformal blocks in CFT. The proof is based on an identity in the algebra with two generators x, y and defining relation xy = yx + yy.