Auto-equivalences of the modular tensor categories of type A, B, C and G
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DOI: 10.1016/j.aim.2022.108364
Abstract: We compute the monoidal and braided auto-equivalences of the modular tensor categories $\mathcal{C}(\mathfrak{sl}_{r+1},k)$, $\mathcal{C}(\mathfrak{so}_{2r+1},k)$, $\mathcal{C}(\mathfrak{sp}_{2r},k)$, and $\mathcal{C}(\mathfrak{g}_{2},k)$. Along with the expected simple current auto-equivalences, we show the existence of the charge conjugation auto-equivalence of $\mathcal{C}(\mathfrak{sl}_{r+1},k)$,… read more here.
Keywords: mathfrak mathcal; equivalences modular; mathcal mathfrak; auto ... See more keywords
On the variety of 1-dimensional representations of finite W-algebras in low rank
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DOI: 10.1016/j.jalgebra.2018.03.030
Abstract: Let $\mathfrak g$ be a simple Lie algebra over $\mathbb C$ and let $e \in \mathfrak g$ be nilpotent. We consider the finite $W$-algebra $U(\mathfrak g,e)$ associated to $e$ and the problem of determining the… read more here.
Keywords: low rank; variety; mathcal mathfrak; dimensional representations ... See more keywords