Abstract
Given a quasi-reductive algebraic supergroup G, we use the theory of semisimplifications of symmetric monoidal categories to define a symmetric monoidal functor Φx:Rep(G)→Rep(OSp(1|2)) associated to any given element x∈Lie(G)1¯. For nilpotent elements x, we show that the functor Φx can be defined using the Deligne filtration associated to x. We use this approach to prove an analogue of the Jacobson-Morozov Lemma for algebraic supergroups. Namely, we give a necessary and sufficient condition on odd nilpotent elements x∈Lie(G)1¯ which define an embedding of supergroups OSp(1|2)→G so that x lies in the image of the corresponding Lie algebra homomorphism.
Original language | English |
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Article number | 108240 |
Journal | Advances in Mathematics |
Volume | 398 |
DOIs | |
State | Published - 26 Mar 2022 |
Keywords
- Duflo Serganova functors
- Jacobson-Morozov Lemma
- Lie superalgebra
- Lie supergroup
- Semisimplification
- Tensor categories
ASJC Scopus subject areas
- Mathematics (all)