Diagram categories for Uq-tilting modules at roots of unity

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  • Henning Haahr Andersen, Denmark
  • Daniel Tubbenhauer, Denmark
In this paper we give a diagrammatic category (inspired by Elias' dihedral cathedral) that is a diagrammatic presentation of the category of Uq(sl2)-tilting modules T for q being an l-th root of unity. Moreover, we, following an approach of Soergel and Stroppel, introduce a grading turning T into a graded category Tgr. This grading is a purely "root of unity" phenomena and might lead to new insights about the link, tangle and 3-manifold invariants deduced from T.
In addition, we also give a diagrammatic category for the (now graded) projective endofunctors pEnd(Tgr), indicate how our results could generalize to Uq(sln) and maybe other types and recall/collect some "well-known" facts to give a reasonably self-contained exposition.
Original languageEnglish
PublisherarXiv.org
Number of pages66
Publication statusPublished - 2014

    Research areas

  • Categorification, Quantum Groups, Roots of unity, Diagram categories

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