Modules of constant Jordan type, pullbacks of bundles and generic kernel filtrations

2015/04/08 by Shawn Baland, Baland, Shawn, Kenneth Chan +1
Mathematics · #16G10 #20C20 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1504.01994

openalex publication_date 2015/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 F_i from kE-modules of constant Jordan type to vector bundles on ℙ^r-1(k), constructed by Benson and Pevtsova. For a kE-module M of constant Jordan type, we show that restricting the sheaf F_i(M) to a dimension s-1 linear subvariety of ℙ^r-1(k) is equivalent to restricting M along a corresponding rank s shifted subgroup of kE and then applying F_i. In the case r=2, we examine the generic kernel filtration of M in order to show that F_i(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.

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