#### Vol. 12, No. 8, 2018

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Categorical representations and KLR algebras

### Ruslan Maksimau

Vol. 12 (2018), No. 8, 1887–1921
##### 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 ${\stackrel{˜}{\mathfrak{s}\mathfrak{l}}}_{e+1}$ contains a subcategory with an action of ${\stackrel{˜}{\mathfrak{s}\mathfrak{l}}}_{e}$. We also give generalizations of these results to more general quivers and Lie types.

##### Keywords
KLR algebra, categorical representation, Hecke algebra, affine Lie algebra, quiver variety, flag variety
##### Mathematical Subject Classification 2010
Primary: 16G99
Secondary: 17B67, 18E10