An explicit construction of the Weyl module as a quotient of symmetric tensors by dual Garnir relations

Abstract

The Weyl modules are the standard modules for the Schur algebra. Their duals (the costandard modules) have well-known constructions as quotients of exterior powers and as submodules of symmetric powers. This paper presents analogous constructions for the Weyl modules themselves, introducing relations that are a non-trivial dualisation of the Garnir relations. More generally, our constructions describe endofunctors on the category of representations of any group.