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 conjecture.
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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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Towards interpolating categories for equivariant map algebras
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 conjecture.