SL2 tilting modules in the mixed case

Louise Sutton ^[1] ; Daniel Tubbenhauer ^[2] ; Paul Wedrich ^[3] ; Jieru Zhu ^[1]
1. [1] Okinawa Institute of Science and Technology
  
  Okinawa Institute of Science and Technology
  
  Japón
2. [2] University of Sydney
  
  University of Sydney
  
  Australia
3. [3] University of Hamburg
  
  University of Hamburg
  
  Hamburg, Freie und Hansestadt, Alemania
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 3, 2023
Idioma: inglés
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Resumen
- Using the non-semisimple Temperley–Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for SL2 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.