Symmetries of ${\mathfrak{gl}}_N$-foams

Abstract

We give an action of a Lie subalgebra of the Witt algebra on foams. This action is compatible with the ${\mathfrak{gl}}_N$-foam evaluation formula. In particular, this endows states spaces associated with ${\mathfrak{gl}}_N$-webs with an ${\mathfrak{sl}}_2$-action. When working in positive characteristic, this can be used to define a $p$-DG structure on these state spaces.

v1: 34 pages, many figures. Comments welcome! v2: 35 pages, exposition improved following referee's comments

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