Categorical representations and KLR algebras

Maksimau, Ruslan

doi:10.2140/ant.2018.12.1887

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Categorical representations and KLR algebras

Ruslan Maksimau

Vol. 12 (2018), No. 8, 1887–1921

DOI: 10.2140/ant.2018.12.1887

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 ${\tilde{s l}}_{e + 1}$ contains a subcategory with an action of ${\tilde{s l}}_{e}$ . 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

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

Vol. 12, No. 8, 2018