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arXiv · 2105.07724

SL2 tilting modules in the mixed case

Louise Sutton·Daniel Tubbenhauer·Paul Wedrich·Jieru Zhu
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Abstract

Using the non-semisimple Temperley-Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for $\mathrm{SL}_{2}$ in the mixed case. This simultaneously generalizes the semisimple situation, the case of the complex quantum group at a root of unity, and the algebraic group case in positive characteristic. We describe character formulas and give a presentation of the category of tilting modules as an additive category via a quiver with relations. Turning to the monoidal structure, we describe fusion rules and obtain an explicit recursive description of the appropriate analog of Jones-Wenzl projectors.

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Louise Sutton, Daniel Tubbenhauer, Paul Wedrich, Jieru Zhu. 2021-05-17. SL2 tilting modules in the mixed case. https://doi.org/10.1007/s00029-023-00835-0

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