Representations of elementary abelian p-groups and bundles on Grassmannians

Jon F. Carlson, Eric M. Friedlander and Julia Pevtsova

Abstract. We initiate the study of representations of elementary abelian p-
groups via restrictions to truncated polynomial subalgebras of the group alge-
bra generated by r nilpotent elements, k[t_1,...,t_r]/(t_1^p,...,t_r^p). We introduce
new geometric invariants based on the behavior of modules upon restrictions
to such subalgebras. We also introduce modules of constant radical and socle
type generalizing modules of constant Jordan type and provide several gen-
eral constructions of modules with these properties. We show that modules of
constant radical and socle type lead to families of algebraic vector bundles on
Grassmannians and illustrate our theory with numerous examples.