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Diagrammatics for $F_4$

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arxiv 2107.12464 v3 pith:DDO2ZE3P submitted 2021-07-26 math.RT math.CT

Raj Gandhi , Alistair Savage , Kirill Zainoulline This is my paper · ORCID
classification math.RTmath.CT
keywords categorytypediagrammaticmonoidalalgebraanalogousbrauercategories
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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.

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  1. Towards interpolating categories for equivariant map algebras

    math.RT 2025-04 conditional novelty 7.0 of 10

    Categorical modules for (equivariant) map algebras are defined diagrammatically, and a candidate interpolating category Curr(OB) for current gl_n-modules is constructed, with its central fullness property left as a co...

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