Constructs an action of the positive Witt algebra on categorified quantum groups for simply-laced Lie algebras, recovering the foam action in type A and inducing the current-algebra action via trace decategorification.
A closed formula for the evaluation of $\mathfrak{sl}_N$-foams
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abstract
We give a purely combinatorial formula for evaluating closed decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral equivariant version of the $\mathfrak{sl}_N$ link homology categorifying the $\mathfrak{sl}_N$ link polynomial. We also provide connections to the equivariant cohomology rings of partial flag manifolds.
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Action of the Witt algebra on categorified quantum groups
Constructs an action of the positive Witt algebra on categorified quantum groups for simply-laced Lie algebras, recovering the foam action in type A and inducing the current-algebra action via trace decategorification.