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arXiv · 1901.11026

Categorical representations and KLR algebras

Ruslan Maksimau
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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 $\widetilde{\mathfrak{sl}}_{e+1}$ contains a subcategory with an action of $\widetilde{\mathfrak{sl}}_{e}$. We also give generalizations of these results to more general quivers and Lie types.

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BibTeXRIS

Ruslan Maksimau. 2019-01-30. Categorical representations and KLR algebras. https://doi.org/10.2140/ant.2018.12.1887

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