``Mass formulae'' for tensor operators connected with Lie superalgebras
Let \({\mathfrak g}\) be a finite-dimensional complex Lie superalgebra and let E and F be finite-dimensional graded \({\mathfrak g}\)-modules. It is well- known that L(F), the space of all linear mappings of F into itself, carries a canonical structure of a graded g-module. A tensor operator of type E and operating in F is a homomorphism of the graded \({\mathfrak g}\)- module E into the graded \({\mathfrak g}\)-module L(F). The author considers the case where the Lie algebra \({\mathfrak g}_{\bar 0}\) of \({\mathfrak g}\) is semisimple and where E is the adjoint \({\mathfrak g}\)- module. Using the Weyl group W of \({\mathfrak g}_{\bar 0}\) he derives certain relations between matrix elements of such tensor operators. (Unfortunately, the author's statements concerning the action of W on \({\mathfrak g}\) and, more generally, on arbitrary \({\mathfrak g}\)-modules, are not correct. Nevertheless, I think his main results should be true.)
scientific article; zbMATH DE number 4142268
scientific article