Year: 2025
Type: article
Abstract: By considering a suitable renormalization of the Temperley–Lieb category, we study its specialization to the case . Unlike the case, the obtained monoidal category, , is not rigid or braided. We provide a closed formula for the Jones–Wenzl projectors in and give semisimple bases for its endomorphism algebras. We explain how to obtain the same basis using the representation theory of finite inverse monoids, via the associated Möbius inversion. We then describe a coboundary structure on and show that its idempotent completion is coboundary monoidally equivalent to the category of ‐crystals. This gives a diagrammatic description of the commutor for ‐crystals defined by Henriques and Kamnitzer and of the resulting action of the cactus group. We also study fiber functors of and discuss how they differ from the case.
DOI: 10.1112/jlms.70283
Authors: Moaaz Alqady, Mateusz Stroiński
Institutions: University of Oregon, Uppsala University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,930
OpenAlex ID: W4414145356