Abstract
We describe a categorical g action, called a (g,theta) action, which is easier to check in practice. Most categorical g actions can be shown to be of this form. The main result is that a (g,theta) action carries actions of quiver Hecke algebras (KLR algebras). We discuss applications of this fact to categorical vertex operators, affine Grassmannians (or Nakajima quiver varieties) and to homological knot invariants.
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