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.

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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