SL2 tilting modules in the mixed case

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.

54 pages, v2 corresponds to the version accepted for publication plus three appendices with additional material and an erratum that corrects missing scalars in Definition 4.7 and the proof of Lemma 4.14

References in corpus (3)

• The Modular Temperley-Lieb Algebra
• $(\ell ,p)$-Jones-Wenzl Idempotents
• Modular Valenced Temperley-Lieb Algebras

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