Quantum diagrammatics for $F_4$

Alistair Savage; Bruce W. Westbury

Quantum diagrammatics for $F_4$

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arxiv 2204.11976 v4 pith:O4QK72G4 submitted 2022-04-25 math.QA math.CTmath.RT

Alistair Savage , Bruce W. Westbury This is my paper · ORCID

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keywords representationalgebracalculuscategorydescriptiondiagrammaticdiagrammaticsdimensional

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abstract

We introduce a graphical calculus for the representation theory of the quantized enveloping algebra of type $F_4$. We do this by giving a diagrammatic description of the category of invariant tensors on the 26-dimensional fundamental representation.

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The quantum spin Brauer category
math.QA 2025-04 accept novelty 7.0 of 10

The quantum spin Brauer category is a braided diagrammatic category whose Karoubi completion covers all finite-dimensional U_q(so(N)) and U_q(o(N)) modules, including spin modules.

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