Quantum diagrammatics for \(F_4\) (Q6564642)

In [Bull. Lond. Math. Soc. 55, No. 1, 349--374 (2023; Zbl 1519.18010)] \textit{R. Gandhi} et al. defined a diagrammatic monoidal category, together with a full and essentially surjective monoidal functor from this category to the category of modules over the exceptional Lie algebra of type \(F_4\). Thus, obtaining a set of diagrammatic tools for studying type \(F_4\) representation theory analogous to those of the oriented and unoriented Brauer categories in classical type.\N\NThe authors of the paper under review generalize the work in [loc. cit.] by developping a quantum version of the diagrammatics. Precisely, they introduce a graphical calculus for the representation theory of the quantized enveloping algebra of type \(F_4\). This is achieved by diagrammatic description of the category of invariant tensors on the 26-dimensional fundamental representation.