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 ${\stackrel{˜}{\mathfrak{s}\mathfrak{l}}}_{e+1}$ 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.

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