Quantum groups and Nichols algebras acting on conformal field theories

We prove that certain screening operators in conformal field theory obey the algebra relations of a corresponding Nichols with diagonal braiding. Our result proves particular long-standing expectation Borel parts small quantum groups appear as operators. The proof is based on novel, intimate relation between Hopf algebras, vertex algebras and class multivalued analytic special functions, which are generalizations Selberg integrals. zeroes these functions correspond to respective algebra, by proving an analytical symmetrizer formula for functions. Moreover, poles encode module extensions Weyl group action. At other poles, fails generate extension algebra. intended application our conjectural logarithmic Kazhdan-Lusztig correspondence. More generally, seems suggest non-local arbitrary should be described appropriate just local can Lie algebras.