Diagrammatics for $F_4$

Abstract

We define 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 $F_4$. In this way, we obtain a set of diagrammatic tools for studying type $F_4$ representation theory that are analogous to those of the oriented and unoriented Brauer categories in classical type.

arXiv comment20 pages. v2: Minor corrections, references added, proof of Prop. 5.2 modified; v3: Small improvements

References in corpus (5)

• Spiders for rank 2 Lie algebras
• Webs and quantum skew Howe duality
• A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
• Invariant tensors for the spin representation of so(7)
• Rational R-matrices, centralizer algebras and tensor identities for e_6 and e_7 exceptional families of Lie algebras

Cited by in corpus (1)

• Quantum diagrammatics for $F_4$