Indecomposable representations of the Lie algebra of derivations for \(d\)-torus
There is a classical functor from the category of finite-dimensional \(\mathfrak{gl}_d\)-modules to the category of modules over the Lie algebra of derivations of the \(d\)-dimensional torus, constructed by \textit{T. A. Larsson} in [Conformal fields: a class of representations of \(\text{Vect}(N)\)'', Int. J. Mod. Phys. A 7, No. 26, 6493--6508 (1992; Zbl 0972.17502)]. In the paper under review the authors study the images of indecomposable finite-dimensional \(\mathfrak{gl}_d\)-modules under this functor. They show that these images are always indecomposable and most often uniserial. In the case when the module is uniserial, its unique composition series is described in details.
scientific article; zbMATH DE number 5692414