Categorification of the colored $\mathfrak{sl}_3$ -invariant

preprint2015arXivOpen access

We give explicit resolutions of all finite dimensional, simple $U_q(\mathfrak{sl_3})$ -modules. We use these resolutions to categorify the colored $\mathfrak{sl}_3$ -invariant of framed links via a complex of complexes of graded $\mathbb{Z}$ -modules.

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Categorification of the colored $\mathfrak{sl}_3$ -invariant

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Categorification of the colored sl3\mathfrak{sl}_3sl3​-invariant

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Categorification of the colored $\mathfrak{sl}_3$ -invariant