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- W2968969917 abstract "Let (mathrm{U}_q({{mathfrak {g}}})) be the quantum supergroup of ({mathfrak {gl}}_{m|n}) or the modified quantum supergroup of ({mathfrak {osp}}_{m|2n}) over the field of rational functions in q, and let (V_q) be the natural module for (mathrm{U}_q({{mathfrak {g}}})). There exists a unique tensor functor associated with (V_q), from the category of ribbon graphs to the category of finite dimensional representations of (mathrm{U}_q({{mathfrak {g}}})), which preserves ribbon category structures. We show that this functor is full in the cases ({{mathfrak {g}}}={mathfrak {gl}}_{m|n}) or ({mathfrak {osp}}_{2ell +1|2n}). For ({{mathfrak {g}}}={mathfrak {osp}}_{2ell |2n}), we show that the space is spanned by images of ribbon graphs if (r+s< 2ell (2n+1)). The proofs involve an equivalence of module categories for two versions of the quantisation of (mathrm{U}({{mathfrak {g}}}))." @default.
- W2968969917 created "2019-08-22" @default.
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- W2968969917 date "2019-08-08" @default.
- W2968969917 modified "2023-10-16" @default.
- W2968969917 title "First fundamental theorems of invariant theory for quantum supergroups" @default.
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- W2968969917 doi "https://doi.org/10.1007/s40879-019-00360-5" @default.
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