Irreducible representations of the Lie-algebra of the diffeomorphisms of a \(d\)-dimensional torus (Q1922468)

This paper discusses the irreducibility of certain modules associated with the Lie algebra of diffeomorphisms of the \(d\)-dimensional torus. First, the paper regards the above diffeomorphisms as derivations of a Laurent polynomial ring \(A\) in \(d\) variables and recalls a functor from the \(gl_d\)-modules to the (Der \(A)\)-modules (where \(gl_d\) is the Lie algebra of \(d \times d\) complex matrices). Then, the paper shows that the image of a finite-dimensional irreducible \(gl_d\)-module is most often irreducible. The only exceptions are fundamental modules and one dimensional modules. The paper is motivated by some problems related to the Virasoro algebra.