MODULES OF CONSTANT JORDAN TYPE, PULLBACKS OF BUNDLES AND GENERIC KERNEL FILTRATIONS
SHAWN BALAND AND KENNETH CHAN
Abstract. Let kE denote the group algebra of an elementary abelian p-group of rank r
over an algebraically closed field of characteristic p. We investigate the functors Fi from
kE-modules of constant Jordan type to vector bundles on Pr-1(k), constructed by Benson
and Pevtsova. For a kE-module M of constant Jordan type, we show that restricting the
sheaf F (M) to a dimension s - 1 linear subvariety of Pr-1(k) is equivalent to restricting i
M along a corresponding rank s shifted subgroup of kE and then applying Fi.
In the case r = 2, we examine the generic kernel filtration of M in order to show that Fi(M) may be computed on certain subquotients of M whose Loewy lengths are bounded in terms of i. More precise information is obtained by applying similar techniques to the nth power generic kernel filtration of M. The latter approach also allows us to generalise
our results to higher ranks r.