Quantum Berezinian and the classical Capelli identity
For the quantum deformation of the Lie superalgebra \({\mathfrak gl}(m| n)\) the analogue of the determinant - quantum Berezinian - is constructed by a new method leading to a ``super'' analog of the Capelli identity and a conjectorial description of the center of \(U_ q({\mathfrak gl}(m| n))\). The proof, based on a (quantum, super) version of Howe's duality, is to be published.
scientific article; zbMATH DE number 4189969