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DIAGRAM CATEGORIES FOR Uq-TILTING MODULES AT ROOTS OF UNITY

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Abstract

We give a diagrammatic presentation of the category of U q (\( \mathfrak{s}\mathfrak{l} \) 2)-tilting modules for q being a root of unity and introduce a grading on . This grading is a “root of unity phenomenon” and might lead to new insights about link and 3-manifold invariants deduced from . We also give a diagrammatic category for the (graded) projective endofunctors on , indicate how our results could generalize, and collect some “well-known” facts to give a reasonably self-contained exposition.

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  1. Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark

    H. H. ANDERSEN & D. TUBBENHAUER

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ANDERSEN, H.H., TUBBENHAUER, D. DIAGRAM CATEGORIES FOR Uq-TILTING MODULES AT ROOTS OF UNITY. Transformation Groups 22, 29–89 (2017). https://doi.org/10.1007/s00031-016-9363-z

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