On classical tensor categories attached to the irreducible representations of the General Linear Supergroups $GL(n\vert n)$

We study the quotient of $T_{n} = R e p (G L (n ∣ n))$ by the tensor ideal of negligible morphisms. If we consider the full subcategory $T_{n}^{+}$ of $T_{n}$ of indecomposable summands in iterated tensor products of irreducible representations up to parity shifts, its quotient is a semisimple tannakian category $R e p (H_{n})$ where $H_{n}$ is a pro-reductive algebraic group. We determine the connected derived subgroup $G_{n} \subset H_{n}$ and the groups $G_{λ} = (H_{λ}^{0})_{d e r}$ corresponding to the tannakian subcategory in $R e p (H_{n})$ generated by an irreducible representation $L (λ)$ . This gives structural information about the tensor category $R e p (G L (n ∣ n))$ , 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 $π_{0} (H_{n})$ .

On classical tensor categories attached to the irreducible representations of the General Linear Supergroups $G L (n ∣ n)$

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On classical tensor categories attached to the irreducible representations of the General Linear Supergroups $G L (n ∣ n)$

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On classical tensor categories attached to the irreducible representations of the General Linear Supergroups GL(n∣n)GL(n∣n)

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On classical tensor categories attached to the irreducible representations of the General Linear Supergroups GL(n∣n)GL(n∣n)

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On classical tensor categories attached to the irreducible representations of the General Linear Supergroups $G L (n ∣ n)$

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On classical tensor categories attached to the irreducible representations of the General Linear Supergroups $G L (n ∣ n)$

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