Symmetric and Exterior Powers, Linear Source Modules and Representations of Schur Superalgebras

We study modules for the general linear group (over an infinitefield of arbitrary characteristic) which are direct summandsof tensor products of exterior powers and symmetric powers ofthe natural module. These modules, which we call listing modules,include the tilting modules and the injective modules for Schuralgebras. The modules are studied via their relationship tolinear source modules for symmetric groups on the one hand,and simple modules for Schur superalgebras on the other. Listingmodules are parametrized by certain pairs of partitions. Theyare used to describe, by generators and relations, the Grothendieckring of polynomial functors generated by the symmetric and exteriorpowers. We also (continuing work of J. Grabmeier) describe thevertices and sources of linear source modules for symmetricgroups. 2000 Mathematical Subject Classification: 20G05, 20C30.