Categorical representations and KLR algebras

Ruslan Maksimau (1, 2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 UM - Université de Montpellier

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.

Domaines: Théorie des représentations [math.RT]; Catégories et ensembles [math.CT]

Ruslan Maksimau. Categorical representations and KLR algebras. Algebra & Number Theory, 2018, 12 (8), pp.1887-1921. ⟨10.2140/ant.2018.12.1887⟩. ⟨hal-02003132⟩