Séminaires : Séminaire Groupes, Représentations et Géométrie

Motivated by the difficult task of finding low rank indecomposable vector bundles on projective space, we discuss a computational construction strategy for G-equivariant modules over the graded exterior algebra, where G is a finite group. Via an equivariant version of the BGG correspondence, some of these modules can indeed be identified with G-equivariant vector bundles on projective space. For the implementation of our computational construction strategy we use methods of constructive category theory such as a skeletal version of the tensor category of representations of G over a splitting field, and an internalized version of the exterior algebra. These methods are all provided by our computer algebra project CAP (Categories, Algorithms, Programming).