Resumen de On classical tensor categories attached to the irreducible representations of the general linear supergroups GL(n|n)

Thorsten Heidersdorf, Rainer Weissauer

• We study the quotient of Tn = Rep(G L(n|n)) by the tensor ideal of negligible morphisms. If we consider the full subcategory T +n of Tn of indecomposable summands in iterated tensor products of irreducible representations up to parity shifts, its quotient is a semisimple tannakian category Rep(Hn) where Hn is a pro-reductive algebraic group.

  We determine the Hn and the groups Hλ corresponding to the tannakian subcategory in Rep(Hn) generated by an irreducible representation L(λ). This gives structural information about the tensor category Rep(G L(n|n)), including the decomposition law of a tensor product of irreducible representations up to summands of superdimension zero. Some results are conditional on a hypothesis on 2-torsion in π0(Hn).