Categorical representations and KLR algebras

Abstract

We prove that the KLR algebra associated with the cyclic quiver of length $e$ is a subquotient of the KLR algebra associated with the cyclic quiver of length $e+1$. We also give a geometric interpretation of this fact. This result has an important application in the theory of categorical representations. We prove that a category with an action of ${\widetilde{\mathfrak{sl}}}_{e+1}$ contains a subcategory with an action of ${\widetilde{\mathfrak{sl}}}_e$. We also give generalizations of these results to more general quivers and Lie types.

40 pages. arXiv admin note: substantial text overlap with arXiv:1512.04878

References in corpus (2)

• 2-Kac-Moody algebras
• Derived equivalences for symmetric groups and sl\_2-categorification

Cited by in corpus (1)

• Affine category O, Koszul duality and Zuckerman functors