On classical tensor categories attached to the irreducible representations of the general linear supergroups GL(n|n)
We study the quotient of $$\mathcal {T}_n = Rep(GL(n|n))$$by the tensor ideal of negligible morphisms. If we consider the full subcategory $$\mathcal {T}_n^+$$of $$\mathcal {T}_n$$of indecomposable summands in iterated tensor products of irreducible representations up to parity shifts, its quotient...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
20 April 2023
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| In: |
Selecta mathematica
Year: 2023, Volume: 29, Issue: 3, Pages: 1-101 |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-023-00842-1 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s00029-023-00842-1 Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s00029-023-00842-1 
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| Author Notes: | Th. Heidersdorf, R. Weissauer |
| Summary: | We study the quotient of $$\mathcal {T}_n = Rep(GL(n|n))$$by the tensor ideal of negligible morphisms. If we consider the full subcategory $$\mathcal {T}_n^+$$of $$\mathcal {T}_n$$of indecomposable summands in iterated tensor products of irreducible representations up to parity shifts, its quotient is a semisimple tannakian category $$Rep(H_n)$$where $$H_n$$is a pro-reductive algebraic group. We determine the $$H_n$$and the groups $$H_{\lambda }$$corresponding to the tannakian subcategory in $$Rep(H_n)$$generated by an irreducible representation $$L(\lambda )$$. This gives structural information about the tensor category Rep(GL(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 $$\pi _0(H_n)$$. |
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| Item Description: | Gesehen am 31.07.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-023-00842-1 |