Abstract
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.
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Mukhin, E., Varchenko, A. Quantization of the Space of Conformal Blocks. Letters in Mathematical Physics 44, 157–167 (1998). https://doi.org/10.1023/A:1007465401183
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DOI: https://doi.org/10.1023/A:1007465401183