Rigidity in higher representation theory

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.

49 pages

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Cited by in corpus (8)

• Etingof conjecture for quantized quiver varieties
• Deformations of colored sl(N) link homologies via foams
• Categorified skew Howe duality and comparison of knot homologies
• Current algebras and categorified quantum groups
• Curved Rickard complexes and link homologies
• Associated graded of Hodge modules and categorical sl_2 actions
• A categorical action of the shifted $q=0$ affine algebra
• Categorification via blocks of modular representations II