Vol. 12, No. 8, 2018

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Categorical representations and KLR algebras

Ruslan Maksimau

Vol. 12 (2018), No. 8, 1887–1921

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.

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KLR algebra, categorical representation, Hecke algebra, affine Lie algebra, quiver variety, flag variety
Mathematical Subject Classification 2010
Primary: 16G99
Secondary: 17B67, 18E10
Received: 2 May 2016
Revised: 14 February 2018
Accepted: 2 June 2018
Published: 4 December 2018
Ruslan Maksimau
Institut Montpelliérain Alexander Grothendieck
Université de Montpellier