A construction of semisimple tensor categories

Starting from an abelian category A such that every object has only finitely many subobjects we construct a semisimple tensor category T. We show that T interpolates the categories Rep(Aut(p),K) where p runs through certain projective pro-objects of A. The main example is A=finite dimensional F_q-vector spaces. Then T can be considered as the category of representation of GL(n,F_q) where n is not a natural number. This work extends a construction of Deligne for symmetric groups.

Appeared in: Comptes Rendus Mathématique. Académie des Sciences. Paris 343 (2006) 15-18

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Last updated: July 3, 2006