Abstract
We study modules for the general linear group (over an infinite field of arbitrary characteristic) which are direct summands of tensor products of exterior powers and symmetric powers of the natural module. These modules, which we call listing modules, include the tilting modules and the injective modules for Schur algebras. The modules are studied via their relationship to linear source modules for symmetric groups on the one hand, and simple modules for Schur superalgebras on the other. Listing modules are parametrized by certain pairs of partitions. They are used to describe, by generators and relations, the Grothendieck ring of polynomial functors generated by the symmetric and exterior powers. We also (continuing work of J. Grabmeier) describe the vertices and sources of linear source modules for symmetric groups. 2000 Mathematical Subject Classification: 20G05, 20C30.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
