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A stratification of generic representation theory and generalized Schur algebras
 Documenta Mathematica 9 (2004) 41–56 V. Franjou and T. Pirashvili
"... Abstract. If Fq is the finite field of characteristic p and order q = ps, let F(Fq) be the category whose objects are functors from finite dimensional Fq–vector spaces to Fq–vector spaces, and with morphisms the natural transformations between such functors. We define an infinite lattice of thick su ..."
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Abstract. If Fq is the finite field of characteristic p and order q = ps, let F(Fq) be the category whose objects are functors from finite dimensional Fq–vector spaces to Fq–vector spaces, and with morphisms the natural transformations between such functors. We define an infinite lattice of thick subcategories of F(Fq). Our main result then identifies various subquotients as categories of modules over products of symmetric groups, via recollement diagrams. Our lattice of thick subcategories is a refinement of the Eilenberg–MacLane polynomial degree filtration F 0 (Fq) ⊂ F 1 (Fq) ⊂ F 2 (Fq) ⊂... of F(Fq) which has been extensively studied and used in the algebraic K–theory literature. Our main theorem implies a description of F d (Fq)/F d−1 (Fq) that refines and extends earlier results of Pirashvili and others.
Geometry of Infinitesimal Group Schemes
, 1998
"... 1.66> G and finite dimensional rational Gmodules M . These results, obtained with Andrei Suslin and others, are inspired by analogous results for finite groups. Indeed, we anticipate but have yet to realize a common generalization to the context of finite group schemes of our results and those for ..."
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1.66> G and finite dimensional rational Gmodules M . These results, obtained with Andrei Suslin and others, are inspired by analogous results for finite groups. Indeed, we anticipate but have yet to realize a common generalization to the context of finite group schemes of our results and those for finite groups established by D. Quillen [Q1], J. Carlson [C], G. Avrunin and L. Scott [AS], and others. Although there is considerable parallelism between the contexts of finite groups and infinitesimal group schemes, new techniques have been required to work with infinitesimal group schemes. Since the geometry first occuring in the context of finite groups occurs more naturally and with more structure in these recent developments, we expect these developments to offer new insights into the representation theory of finite groups. The most natural examples of infinitesimal group schemes arise as Frobenius kernels of affine algebraic gro