Homotopies for the Generalized Bar Complex Associated to Certain 3-Rowed Weyl Modules

In \cite{BR2}, Buchsbaum and Rota presented a generalized bar complex associated to certain 3-rowed Weyl modules and proved that this complex is in fact a resolution via an induction on the number of overlaps between the second and third rows and a fundamental exact sequence (\cite{AB}). In this paper we study the structure of this resolution by constructing a splitting contracting homotopy for the complexes corresponding to certain shapes. We also use the method of proof to give a basis for the syzygies that is more structured than the basis given in \cite{sano}.