Quantum screening operators and canonical \(q\)-de Rham cocycles (Q1287113)

The author establishes a close connection between certain cohomology spaces of representations of the quantum affine algebra \(U_q(\widehat{sl_2})\) and a twisted \(q\)-de Rham (Jackson-Aomoto) cohomology of configuration spaces using the quantum screening operators. The author starts with considering a certain \(q\)-analog of the Wakimoto modules via bosonization of the quantum affine algebras, using the scalar boson fields. From the same field he constructs the screening operators. Then the author introduces a certain pairing between elements of \(U_q(\widehat{sl_2})\) and operators between the \(q\)-Wakimoto modules. Solving certain difference equations the author obtains solutions, satisfying the cocycle condition. Then, mixing the \(q\)-de Rham complex with a Hochschild complex the author gets the canonical cocycles, which yield canonical maps between the homology groups of the local systems and the Ext-spaces between the representations.