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

References in corpus (3)

• 2-Kac-Moody algebras
• Category O and sl(k) link invariants
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality