QUANTIZATION OF THE SPACE OF CONFORMAL BLOCKS

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