Vol. 12, No. 8, 2018

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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 sl˜e+1 contains a subcategory with an action of sl˜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
Milestones
Received: 2 May 2016
Revised: 14 February 2018
Accepted: 2 June 2018
Published: 4 December 2018
Authors
Ruslan Maksimau
Institut Montpelliérain Alexander Grothendieck
Université de Montpellier
Montpellier
France