The homological coloured sl3 invariant

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• Louis-Hadrien Robert, University of Hamburg
• Wednesday 04 March 2015, 16:30-17:30
• MR12.

If you have a question about this talk, please contact David Stewart.

I will start with a result on sl_3-representations: I will give an explicit resolution of every simple sl_3-module in terms of tensor powers of the fundamental representation and its dual. Then I will recall the sl_3-link homology due to Khovanov and I will explain that the homology of the unknot is naturally endowed with a two structures of sl_3-representation: the fundamental representation and its dual. I will tell how to use these two facts to construct an homology theory which decategorify on the colored sl_3-invariant for framed links. While the construction is pretty natural there is a major technical difficulty because the sl_3-homology is not known to be functorial for foam cobordisms.

This talk is part of the Algebra and Representation Theory Seminar series.

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